Tootfinder

This https://arxiv.org/abs/2306.09536 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On two definitions of wave-front sets for $p$-adic groups
The wave-front set for an irreducible admissible representation of a $p$-adic reductive group is the set of maximal nilpotent orbits which appear in the local character expansion. By Mœglin-Waldspurger, they are also the maximal nilpotent orbits whose associated degenerate Whittaker models are non-zero. However, in the literature there are two versions commonly used, one defining maximality using analytic closure and the other using Zariski closure. We show that these two definitions are non-e…

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.

Nilpotent graphs over skew PBW extensions
Sebasti\'an Higuera, Armando Reyes
https://arxiv.org/abs/2506.00632 https://arxiv.org/p…

Nilpotent graphs over skew PBW extensions
We investigate the diameter and girth of the nilpotent graph for skew PBW extensions over $2$-primal rings, generalizing similar results on skew polynomial rings. Under certain compatibility conditions, we establish bounds for the diameter of the nilpotent graph and prove invariance of the girth under polynomial extensions.

On an extension of Shlyk's theorem
Jiangtao Shi, Fanjie Xu, Na Li
https://arxiv.org/abs/2506.02885 https://arxiv.org/pdf/2506.028…

On an extension of Shlyk's theorem
In this paper, we prove that the intersection of all non-nilpotent maximal subgroups of a non-solvable group containing the normalizer of some Sylow subgroup is nilpotent, which provides an extension of Shlyk's theorem.

"There are hells on earth and Dubai is one: an infernal creation born of the worst of human tendencies."
https://newleftreview.org/sidecar/posts/everything-else

Caitlín Doherty, Everything Else — Sidecar
In Dubai.

This https://arxiv.org/abs/2503.22664 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Identities of relatively free algebras of Lie nilpotent associative algebras
In this paper, we consider the relatively free algebra of rank $n$, $F_n(\mathfrak{N}_p)$, in the variety of Lie nilpotent associative algebras of index $p$, denoted by $\mathfrak{N}_p$, over a field of characteristic zero. We describe an explicit minimal basis for the polynomial identities of $F_n(\mathfrak{N}_p)$ when $p=3$ and $p=4$, for all $n$, except for $F_3(\mathfrak{N}_4)$. In the general case, we exhibit a lower and an upper bound for the minimal $k$ such that $[x_1,x_2]\cdots[x_{2k-1…

The flat semirings with nilpotent multiplicative reducts
Zidong Gao, Miaomiao Ren
https://arxiv.org/abs/2506.23047 https://arxiv.org/…

The flat semirings with nilpotent multiplicative reducts
In this paper, we focus on the variety $\mathbf{NF}_3$ generated by all flat semirings with $3$-nilpotent multiplicative reducts. By introducing graph semirings, we characterize all subdirectly irreducible members of $\mathbf{NF}_3$. We prove that the variety $\mathbf{NF}_3$ has uncountably many subvarieties and show that every finitely generated subvariety of $\mathbf{NF}_3$ is a Cross variety. Moreover, we demonstrate that $\mathbf{NF}_3$ has a unique limit subvariety, which is generated by a…

Rings Whose Non-Units are Square-Nil Clean
Mina Doostalizadeh, Ahmad Moussavi, Peter Danchev
https://arxiv.org/abs/2508.01286 https://arxiv.org/pdf/2508.01…

Rings Whose Non-Units are Square-Nil Clean
We consider in-depth and characterize in certain aspects the class of so-called {\it strongly NUS-nil clean rings}, that are those rings whose non-units are {\it square nil-clean} in the sense that they are a sum of a nilpotent and a square-idempotent that commutes with each other. This class of rings lies properly between the classes of strongly nil-clean rings and strongly clean rings. In fact, it is proved the valuable criterion that a ring $R$ is strongly NUS-nil clean if, and only if, $a^4…

On Zel'manov's global nilpotence theorem for Engel Lie algebras
Michael Vaughan-Lee
https://arxiv.org/abs/2507.21677 https://arxiv.org/pdf/2507.216…

On Zel'manov's global nilpotence theorem for Engel Lie algebras
I give a proof of Zel'manov's theorem that if $L$ is an $n$-Engel Lie algebra over a field $F$ of characteristic zero then $L$ is (globally) nilpotent. This is a very important result which extends Kostrikin's theorem that $L$ is locally nilpotent if the characteristic of $F$ is zero or some prime $p>n$. Zel'manov's proof contains some striking original ideas, and I wrote this note in an effort to understand his arguments. I hope that my efforts will be of use to other mathematicians in underst…

Nilpotent primitive linear groups over finite fields
A. S. Detinko, D. L. Flannery
https://arxiv.org/abs/2507.20628 https://arxiv.org/pdf/2507.20628…

Nilpotent primitive linear groups over finite fields
We provide a detailed structural description of the nilpotent primitive subgroups of $\mathrm{GL}(n, \mathbb{F})$, where $\mathbb{F}$ is a finite field.