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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.

Entanglement-enhanced optical ion clock
Kai Dietze (Physikalisch-Technische Bundesanstalt, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover, Hannover, Germany), Lennart Pelzer (Physikalisch-Technische Bundesanstalt), Ludwig Krinner (Physikalisch-Technische Bundesanstalt, Institut f\"ur Quantenoptik, Leibniz Universit\"at Hannover, Hannover, Germany), Fabian Dawel (Physikalisch-Technische Bundesanstalt, Institut f\"ur Quantenoptik, Leibniz Universit\&…

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

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/

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…

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…

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…

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…

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

Diffraction phase-free Bragg atom interferometry
V\'ictor J. Mart\'inez Lahuerta (Leibniz University Hannover, Institute of Quantum Optics, Hannover, Germany), Jan-Niclas Kirsten-Siem{\ss} (Leibniz University Hannover, Institute of Quantum Optics, Hannover, Germany), Klemens Hammerer (Leibniz University Hanover), Naceur Gaaloul (Leibniz University Hannover, Institute of Quantum Optics, Hannover, Germany)

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.

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…

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 $…

Associative triple trisystems and standard embeddings
Ra\'ul Felipe, Guillermo Vera de Salas
https://arxiv.org/abs/2506.04191 https://

Associative triple trisystems and standard embeddings
Building on the established theories of Jordan triple disystems and Leibniz triple systems, we introduce and develop the theory of associative triple trisystems, filling a significant gap in the existing framework. We establish the classical relationships between associative, Jordan, and Lie triple systems within the context of trisystems. We present a significant example by equipping the space of matrices with a non-trivial associative dialgebra structure. We conclude defining the concept of d…

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…