Tootfinder

From $n$-Leibniz algebras and linear $n$-racks to the solutions of the (higher analogue of) Yang-Baxter equation
Apurba Das, Suman Majhi
https://arxiv.org/abs/2508.07005 https:/…

From $n$-Leibniz algebras and linear $n$-racks to the solutions of the (higher analogue of) Yang-Baxter equation
In this paper, we first demonstrate that a finite-dimensional $n$-Leibniz algebra naturally gives rise to an $n$-rack structure on the underlying vector space. Given any $n$-Leibniz algebra, we also construct two Yang-Baxter operators on suitable vector spaces and connect them by a homomorphism. Next, we introduce linear $n$-racks as the coalgebraic version of $n$-racks and show that a cocommutative linear $n$-rack yields a linear rack structure and hence a Yang-Baxter operator. An $n$-Leibniz …

A Lie Bracket on the Space of (Right) Biderivations of a Lie Algebra
Alfonso Di Bartolo, Gianmarco La Rosa
https://arxiv.org/abs/2507.12089 https://…

A Lie Bracket on the Space of (Right) Biderivations of a Lie Algebra
Derivations extend the concept of differentiation from functions to algebraic structures as linear operators satisfying the Leibniz rule. In Lie algebras, derivations form a Lie algebra via the commutator bracket of linear endomorphisms. Motivated by this, we study biderivations-bilinear maps capturing higher-order infinitesimal symmetries. This work focuses on right biderivations of Lie algebras, introducing Lie brackets on spaces of biderivations to explore their algebraic and geometric prope…

Temperature-compensating package for OH line filters for astronomy: II. manufacture, assembly, and performance study
Xijie Luo (Leibniz Institute for Astrophysics Potsdam, Institut f\"ur Physik und Astronomie, Universit\"at Potsdam, Potsdam, Germany), Carlos E. Rodriguez Alvarez (Leibniz Institute for Astrophysics Potsdam, Technische Universit\"at Berlin, Fakult\"at V- Institut f\"ur Mechanik, FG Strukturmechanik und Strukturberechnung, Berlin, Germany), Aashia…

Temperature-compensating package for OH line filters for astronomy: II. manufacture, assembly, and performance study
Multi-channel aperiodic fiber Bragg grating (FBG) based hydroxyl (OH) line filters have attracted significant interest in ground-based near-infrared (NIR) astronomical observations. In this paper, we present the performance of a new self-compensating enclosure for the filters, that can be used in non-temperature-controlled environments. Our prototype encloses a 110 mm long single-mode photosensitive optical fiber with three 10 mm filter gratings. A fourth grating was used as a reference outside…

Replaced article(s) found for math.QA. https://arxiv.org/list/math.QA/new
[1/1]:
- Quasi-triangular, triangular, factorizable anti-Leibniz bialgebras and anti-Leibniz Yang-Baxter e...
Bo Hou, Zhanpeng Cui

der erik uden workshop, wo ich beibringe wie man erik uden ist :erikuden:

The Leibniz-Gemeinschaft is now on Mastodon:
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Welcome!

A characterization of perfect Leibniz algebras
Nikolaos Panagiotis Souris
https://arxiv.org/abs/2509.05990 https://arxiv.org/pdf/2509.05990

A characterization of perfect Leibniz algebras
Leibniz algebras are non-antisymmetric generalizations of Lie algebras that have attracted substantial interest due to their close relation with the latter class. A Leibniz algebra $A$ is called perfect if it coincides with its derived subalgebra $A^2$. As a generalization of an analogous result for Lie algebras, we show that perfect Leibniz algebras, of arbitrary dimension and over any field, are characterized among Leibniz algebras by the property that they are ideals whenever they are embedd…

An integration of Lie-Leibniz triples
Ryo Hayami
https://arxiv.org/abs/2508.19143 https://arxiv.org/pdf/2508.19143

An integration of Lie-Leibniz triples
In this paper, we introduce the group version of a Lie-Leibniz triple. We define a Lie group-rack triple whose tangent structure is a Lie-Leibniz triple. This triple is a generalization of an augmented Lie rack. We show that any finite-dimensional Lie-Leibniz triple can be integrated to a local Lie group-rack triple by generalizing the integration procedure of an augmented Leibniz algebra into an augmented Lie rack.

The role of the Lorentz force in sunspot equilibrium: #sunspots - 400-year-old mystery now solved by astrophysicists at the Freiburg Institute of Solar Physics (KIS): https://www.leibniz-kis.de/en/news/article/die-stabilitaet-von-sonnenflecken-wissenschaftler-und-wissenschaftlerinnen-am-institut-fuer-sonnenphysik-kis-in-freiburg-loesen-ein-400-jahre-altes-raetsel/

The heart of NGC 5253 as seen with MUSE-NFM: nitrogen enrichment through stellar chemical feedback at parsec scales
Brigitte G. A. Pruijt (Leiden Observatory, Leiden University), Ana Monreal-Ibero (Leiden Observatory, Leiden University), Peter M. Weilbacher (Leibniz-Institut fur Astrophysik Potsdam), Jeremy R. Walsh (European Southern Observatory), Sebastian Kamann (Astrophysics Research Institute, Liverpool John Moores University), Azlizan A. Soemitro (Leibniz-Institut fur Astrophysik…

The heart of NGC 5253 as seen with MUSE-NFM: nitrogen enrichment through stellar chemical feedback at parsec scales
NGC 5253 is a nearby (D=3.6 Mpc) Blue Compact Dwarf galaxy, notable for its three massive young super star clusters (SSCs) and nitrogen enrichment. Its similarity to extreme star-forming galaxies at high redshift makes it a good local analogue for studying chemical enrichment at high spatial resolution. We characterise the ionised gas and dust in the giant HII region in the proximity of the three SSCs in the centre of NGC 5253 using new Multi-Unit Spectroscopic Explorer Narrow Field Mode adapti…

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
Benoit Cloitre
https://arxiv.org/abs/2507.20428 https://arxiv.org/pdf/2507.20428…

A BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series
We derive a BBP-type formula for the remainder of the Madhava-Gregory-Leibniz series for $π$. The result is a closed form in base-$16$ with Pochhammer denominators. The analogous formula for the alternating series for $\log 2$ is also presented.

These: "Mähroboter töten Igel"
Der Verein "Pro Igel e.V." hat dazu dies:
"Im Zeitraum September 2021 bis September 2024 hat das Leibniz-Institut für Zoo- und Wildtierforschung (Leibniz-IZW) anhand von 370 deutschlandweit gemeldeten Einzelfällen verletzter Tiere festgestellt, dass knapp die Hälfte die Verletzung durch Mähroboter oder Freischneider nicht überlebt hat."
Dieser seltsam konstruierte Satz verdeckt nur notdürftig: Die haben eigentlich…

Likelihood Functions with Parameter-Dependent Support: A Survey of the Cram\'{e}r-Rao-Leibniz Lower Bound
Qin Lu, Yaakov Bar-Shalom, Peter Willett
https://arxiv.org/abs/2508.01145

Likelihood Functions with Parameter-Dependent Support: A Survey of the Cramér-Rao-Leibniz Lower Bound
Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the estimator. In this regard, the Cramér-Rao lower bound (CRLB) is of great importance, as it provides a lower bound on the variance of {\it any} unbiased estimator. In many cases, it is the only way of evaluating, without recourse to simulations, the expected a…

Affinization of algebraic structures: Leibniz algebras
Tomasz Brzezi\'nski, Krzysztof Radziszewski, Brais Ramos P\'erez
https://arxiv.org/abs/2506.23398

Affinization of algebraic structures: Leibniz algebras
A general procedure of affinization of linear algebra structures is illustrated by the case of Leibniz algebras. Specifically, the definition of an affine Leibniz bracket, that is, a bi-affine operation on an affine space that at each tangent vector space becomes a (bi-linear) Leibniz bracket in terms of a tri-affine operation called a Leibnizian, is given. An affine space together with such an operation is called a Leibniz affgebra. It is shown that any Leibniz algebra can be extended to a fam…

Leibniz $2$-algebras, linear $2$-racks and the Zamolodchikov Tetrahedron equation
Nanyan Xu, Yunhe Sheng
https://arxiv.org/abs/2506.16714 https://

Leibniz $2$-algebras, linear $2$-racks and the Zamolodchikov Tetrahedron equation
In this paper, first we show that a central Leibniz 2-algebra naturally gives rise to a solution of the Zamolodchikov Tetrahedron equation. Then we introduce the notion of linear 2-racks and show that a linear 2-rack also gives rise to a solution of the Zamolodchikov Tetrahedron equation. We show that a central Leibniz 2-algebra gives rise to a linear 2-rack if the underlying 2-vector space is splittable. Finally we discuss the relation between linear 2-racks and 2-racks, and show that a linear…

Doch lieber Katzen-Content? Laut Leibniz-Institut für Medienforschung entziehen sich immer mehr Menschen den Nachrichten: 71% tun dies gelegentlich, weil die Düsternis auf die Stimmung drückt oder sie schlicht ermüden. Eine Entwicklung, die nachvollziehbar ist – aber auch bedenklich #T-online

Abelian extensions of five-dimensional solvable Leibniz algebras
A. Kh. Khudoyberdiyev, S. A. Sheraliyeva
https://arxiv.org/abs/2506.23528 https://

Abelian extensions of five-dimensional solvable Leibniz algebras
In this work, we extend the central extension method for solvable Leibniz algebras. Using this method, a complete classification of one-dimensional abelian extensions of five-dimensional solvable Leibniz algebras with a non-trivial three-dimensional nilradical is obtained. Furthermore, we explore extensions of solvable Leibniz algebras whose nilradical is null-filiform, establishing that, in this case, there exists a unique solvable abelian extension.

Mechanical Characterisation of Silicon for the ETpathfinder Test Masses
Guido Alex Iandolo, Alex Amato, Gianpietro Cagnoli, Alessandro Delmonte, Jan-Simon Hennig, Margot Hennig, Sebastian Steinlechner, Janis W\"ohler, Stefan Hild, Jessica Steinlechner
https://arxiv.org/abs/2508.03468

Mechanical Characterisation of Silicon for the ETpathfinder Test Masses
The next generation of gravitational-wave detectors, such as the Einstein Telescope, is designed to reduce noise in a wide band of frequencies compared to the current generation, through the use of new technologies. ETpathfinder, designed as an R&D facility for these technologies, is a prototype for which the mirrors were chosen to be made of crystalline silicon, produced by the Leibniz-Institut für Kristallzüchtung. This material choice was made to pave the way for a low thermal noise level …

Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras
Wen Teng
https://arxiv.org/abs/2508.15775 https://arxiv.org/pdf/2508.15775

Twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras
The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted Rota-Baxter operators, and we define the cohomology of a twisted Rota-Baxter operator. Then we consider formal and order $n$ deformations of twisted Rota-Baxter operators from cohomological points of view. Finally, we introduce and study NS-3-Leibniz algebras as the …

Post-compression of a Q-switched laser in a glass-rod multi-pass cell
Peer Biesterfeld (Leibniz University Hannover, Institute of Quantum Optics, Welfengarten 1, Hannover, Germany), Arthur Sch\"onberg (Deutsches Elektronen-Synchrotron DESY, Notkestra{\ss}e 85, 22607 Hamburg, Germany), Marc Seitz (Center for Free-Electron Laser Science CFEL, Deutsches Elektronen-Synchrotron DESY, Notkestra{\ss}e 85, Hamburg, Germany), Nayla Jimenez (Deutsches Elektronen-Synchrotron DESY, Notkestra{…

Post-compression of a Q-switched laser in a glass-rod multi-pass cell
Q-switched lasers are compact, cost-effective, and highly pulse energy-scalable sources for nanosecond-scale laser pulses. The technology has been developed for many decades and is widely used in scientific, industrial and medical applications. However, their inherently narrow bandwidth imposes a lower limit on pulse duration - typically in the few-hundred-picosecond range - limiting the applicability of Q-switched technology in fields that require ultrafast laser pulses in the few-picosecond o…

Biderivations of some classes of solvable Leibniz algebras
Bakhtiyor Yusupov, Doston Jumaniyozov, Majidkhon Azizov
https://arxiv.org/abs/2507.18134 https://

Biderivations of some classes of solvable Leibniz algebras
In this work, we investigate anti-derivations and biderivation of Leibniz algebras. We describe general form of anti-derivations and biderivations on null-filiform and filiform Leibniz algebras. Moreover, we show how to construct Leibniz algebras, while using these biderivations. We describe general form of anti-derivations and biderivations on solvable Leibniz algebras with null-filiform and filiform nilradicals. Interesting fact that, any biderivations of solvable Leibniz algebras with null-f…

The magnetohydrodynamical system in bounded $\mathscr{C}^1$ domains of dimension $n\ge3$
Sylvie Monniaux (I2M,FAMSI - IRL 2032)
https://arxiv.org/abs/2507.18195 https://

The magnetohydrodynamical system in bounded $\mathscr{C}^1$ domains of dimension $n\ge3$
Existence of mild solutions for the magnetohydrodynamical system in $\mathscr{C}^1$ domains is established in critical spaces in dimension $n\ge 3$. The proof relies on recent regularity results on the Stokes operator in $\mathscr{C}^1$ domains and a Leibniz-like formula for differential forms proved here in Section 2.

Leibniz rings: some basic and structural results
L. A. Kurdachenko, O. O. Pypka, M. M. Semko
https://arxiv.org/abs/2508.17319 https://arxiv.org/pdf/2508.17…

Leibniz rings: some basic and structural results
In this paper, we study the fundamental properties of Leibniz rings. Special attention is given to the structure of Leibniz rings whose additive group is "small". The results obtained illustrate a significant difference between the classes of Leibniz rings and Lie rings.

Cohomology theory for matched pairs of Leibniz algebras and its applications
Ying-Hua Lu, Tao Zhang
https://arxiv.org/abs/2508.14044 https://arxiv.org/pdf/…

Cohomology theory for matched pairs of Leibniz algebras and its applications
This paper introduces the concept of representations for matched pairs of Leibniz algebras and develops corresponding cohomology theories, examining how cohomology groups can be applied in the context of matched pairs of Leibniz algebras. Initially, we utilize the cohomology theory to investigate infinitesimal deformations and abelian extensions of matched pairs of Leibniz algebras. Next, given an abelian extension of a matched pair of Leibniz algebras and its representation, we explore the ind…

On $(\delta,f)$-derivations and Jordan $(\delta,f)$-derivations on modules
Gusti Ayu Dwi Yanti, Indah Emilia Wijayanti
https://arxiv.org/abs/2508.07609 https://

On $(δ,f)$-derivations and Jordan $(δ,f)$-derivations on modules
Let $R$ be a ring with identity, $M,N$ right modules over $R$. An additive mapping $δ$ from $R$ to $R$ is called derivation on ring $R$ if it satisfies the Leibniz condition. If $δ$ is a derivation on $R$ and $f:M \rightarrow N$ is a module homomorphism over $R$, then an additive mapping $d:M \rightarrow N$ is called a $(δ,f)$-derivation if it satisfies $d(xa)=d(x)a+f(x)δ(a)$ for all $x \in M$ and $a \in R$. An additive mapping $δ: R \rightarrow R$ is called Jordan derivation on ring $R$ i…

Classification of three-dimensional Nijenhuis Leibniz algebras
Tianshui Ma, Chan Zhao
https://arxiv.org/abs/2507.12692 https://arxiv.…

Classification of three-dimensional Nijenhuis Leibniz algebras
There are thirteen types of three-dimensional Leibniz algebras over the real field $\mathbb{R}$ based on the classification given by S. Ayupov, B. Omirov and I. Rakhimov in [Leibniz algebras: structure and classification. CRC Press, Boca Raton, FL, 2020]. In this paper, we investigate all the Nijenhuis operators on these thirteen types of three-dimensional Leibniz algebras.

The integro-differential closure of a commutative differential ring
Clemens G. Raab, Georg Regensburger
https://arxiv.org/abs/2507.07889 https://

The integro-differential closure of a commutative differential ring
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a generalized evaluation is defined in terms of integration and differentiation. The induced evaluation is not necessarily multiplicative, which allows to model functions with singularities and leads to generalized shuffle relations. In general, not every element of a differential ring has an antiderivative in the same…

Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules
Yan Ning, Daowei Lu, Dingguo Wang
https://arxiv.org/abs/2509.08278 https://arxiv.org/pdf/250…

Fundamental theorem of transposed Poisson $(A,H)$-Hopf modules
Transposed Poisson algebra was introduced as a dual notion of the Poisson algebra by switching the roles played by the commutative associative operation and Lie operation in the Leibniz rule defining the Poisson algebra. Let $H$ be a Hopf algebra with a bijective antipode and $A$ an $H$-comodule transposed Poisson algebra. Assume that there exists an $H$-colinear map which is also an algebra map from $H$ to the transposed Poisson center of $A$. In this paper we generalize the fundamental theore…

Universal Coacting Hopf Algebra of a finite-dimensional Algebra over an Operad
Saikat Goswami, Satyendra Kumar Mishra, Suman Pattanayak
https://arxiv.org/abs/2507.05909

Universal Coacting Hopf Algebra of a finite-dimensional Algebra over an Operad
A. L. Agore and G. Militaru constructed a new invariant (a ``universal coacting Hopf algebra") for some finite-dimensional binary quadratic algebras such as Lie/Leibniz algebras, associative algebras, and Poisson algebras with prominent applications. In this paper, we give a construction of universal coacting bi/Hopf algebra for any finite-dimensional algebra over a symmetric operad $\mathcal{P}$. Precisely, we construct a universal algebra $\mathcal{C}(\mathfrak{a})$ for a finite-dimensional $…

Nonassociative algebras of anti-biderivation-type
Sa\"id Benayadi, Said Boulmane, Ivan Kaygorodov
https://arxiv.org/abs/2506.17228 https://

Nonassociative algebras of anti-biderivation-type
The main purpose of this paper is to study the class of Jacobi-Jordan-admissible algebras, such that its product is an anti-biderivation of the related Jacobi-Jordan algebra. We called it as $\mathcal A{\rm BD}$-algebras. First, we provide characterizations of algebras in this class. Furthermore, we show that this class of nonassociative algebras includes Jacobi-Jordan algebras, symmetric anti-Leibniz algebras, and anti-${\rm LR}$-algebras. In particular, we proved that anti-${\rm LR}$-algebras…