Tootfinder

Rost nilpotence for twisted Milnor hypersurfaces
Charles De Clercq, Evan Marth, Kirill Zainoulline
https://arxiv.org/abs/2510.07095 https://arxiv.org/pdf/2…

Rost nilpotence for twisted Milnor hypersurfaces
We show that the strong Rost nilpotence holds for motives of generic hyperplane sections of twisted Milnor hypersurfaces. Hence, we provide a new family of examples of smooth projective algebraic varieties which satisfy the strong Rost nilpotence principle. As an application, we compute the $p$-canonical dimension for such varieties.

Infinite dimensional analogues of nilpotent and solvable Lie algebras
F. H. Haydarov, B. A. Omirov, G. O. Solijanova
https://arxiv.org/abs/2510.02488 https://

Infinite dimensional analogues of nilpotent and solvable Lie algebras
We study infinite-dimensional analogues of nilpotent and solvable Lie algebras, focusing on the classes of pro-nilpotent, residually nilpotent, pro-solvable and residually solvable Lie algebras. We extend classical triangularization results (Engel's and Lie's theorems) to the pro-setting and establish existence results for the pro-nilpotent radical in pro-solvable algebras and in certain residually solvable algebras. We adapt finite-dimensional construction methods to produce residually solvabl…

Batalin-Fradkin-Vilkovisky Quantization of FLPR model
Ansha S. Nair, Saurabh Gupta
https://arxiv.org/abs/2509.05632 https://arxiv.org/pdf/2509.05632…

Batalin-Fradkin-Vilkovisky Quantization of FLPR model
We quantize the Friedberg-Lee-Pang-Ren (FLPR) model within the framework of Batalin-Fradkin-Vilkovisky (BFV) formalism. We construct the nilpotent Becchi-Rouet-Stora-Tyutin (BRST) charges using constraints and the fermionic gauge-fixing function by means of admissible gauge conditions. We also derive the BRST invariant effective action and corresponding symmetries of the model in both polar and Cartesian coordinates. Additionally, with the help of BRST charge, we demonstrate that the physical s…

On a class of involutive Yang-Baxter groups
H. Meng, A. Ballester-Bolinches, P. Jim\'enez-Seral
https://arxiv.org/abs/2509.06521 https://arxiv.org/pdf/…

On a class of involutive Yang-Baxter groups
A group is called an involutive Yang-Baxter group (IYB-group) if it is isomorphic to the permutation group of an involutive, non-degenerate set-theoretic solution of the Yang-Baxter equation. This paper investigates finite soluble groups whose Sylow subgroups have nilpotency class at most two, addressing Cedó and Okniński's question~\cite{CedoOkninski2025} of whether such groups are IYB-groups. We establish that a finite soluble group with Sylow subgroups of class at most two is an IYB-group …

On UK left strategy.
James Schneider, Building the Party — Sidecar
https://newleftreview.org/sidecar/posts/building-the-party?pc=1693

James Schneider, Building the Party — Sidecar
An interview with James Schneider.

Symmetric modules over the infinite polynomial ring I: nilpotent quotients
Rohit Nagpal, Andrew Snowden, Teresa Yu
https://arxiv.org/abs/2508.04624 https://

Symmetric modules over the infinite polynomial ring I: nilpotent quotients
Cohen proved that the infinite variable polynomial ring $R=k[x_1,x_2,\ldots]$ is noetherian with respect to the action of the infinite symmetric group $\mathfrak{S}$. The first two authors began a program to understand the $\mathfrak{S}$-equivariant algebra of $R$ in detail. In previous work, they classified the $\mathfrak{S}$-prime ideals of $R$. An important example of an $\mathfrak{S}$-prime is the ideal $\mathfrak{h}_s$ generated by $(s+1)$st powers of the variables. In this paper, we study…

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space
Anjali Anjali, Akhil Prakash, Amita Amita, Neeraj Kumar Tomar
https://arxiv.org/abs/2509.00784 https://

Idempotent & Nilpotent Operators and Matrices in Bicomplex Space
This paper explores idempotent and nilpotent operators in bicomplex spaces, focusing on their properties and behavior. We define idempotent and nilpotent matrices in this framework and derive related results. Several theorems are presented to establish conditions for the existence and behavior of bicomplex idempotent and nilpotent operators and bicomplex idempotent matrices.

Learning Barycenters from Signature Matrices
Carlos Am\'endola, Leonard Schmitz
https://arxiv.org/abs/2509.07815 https://arxiv.org/pdf/2509.07815

Learning Barycenters from Signature Matrices
The expected signature of a family of paths need not be a signature of a path itself. Motivated by this, we consider the notion of a Lie group barycenter introduced by Buser and Karcher to propose a barycenter on path signatures. We show that every element of the free nilpotent Lie group is a barycenter of a group sample, where all but one sample element can be fixed arbitrarily. In the case of piecewise linear paths, we study the problem of recovering an underlying path corresponding to the ba…

On the intersections of nilpotent subgroups in simple groups
Timothy C. Burness, Hong Yi Huang
https://arxiv.org/abs/2508.03479 https://arxiv.org/pdf/2508.…

On the intersections of nilpotent subgroups in simple groups
Let $G$ be a finite group and let $H_p$ be a Sylow $p$-subgroup of $G$. A very recent conjecture of Lisi and Sabatini asserts the existence of an element $x \in G$ such that $H_p \cap H_p^x$ is inclusion-minimal in the set $\{H_p \cap H_p^g \,:\, g \in G\}$ for every prime $p$. This has been proved in several special cases, including all sufficiently large symmetric and alternating groups. For a simple group $G$, in view of a theorem of Mazurov and Zenkov from 1996, the conjecture implies the e…

The isotropy group of a derivation on a Danielewski-type algebra
Abdessamad Ahouita, Rene Baltazar, M'hammed El Kahoui, Sergey Gaifullin
https://arxiv.org/abs/2510.07059 htt…

The isotropy group of a derivation on a Danielewski-type algebra
Given an algebraically closed field $k$ of characteristic zero, we consider in this paper $k$-algebras of the form $$A_{c,q}=k[x,y,z]/\big(c(x)z-q(x,y)\big),$$ where $c(x)\in k[x]$ is a polynomial of degree at least two and $q(x,y)\in k[x,y]$ is a quasi-monic polynomial of degree at least two with respect to $y$. We give a complete description of the $k$-automorphism group of $A_{c,q}$ as an abstract group. Moreover, for every non-locally nilpotent $k$-derivation $δ$ of $A_{c,q}$ we prove that…