Tootfinder

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
Kobiljon Abdurasulov, Abror Khudoyberdiyev, Feruza Toshtemirova
https://arxiv.org/abs/2506.05353

The geometric classification of nilpotent Lie-Yamaguti, Bol and compatible Lie algebras
The geometric classifications of complex $4$-dimensional nilpotent Lie-Yamaguti algebras, $4$-dimensional nilpotent Bol algebras, and $4$-dimensional nilpotent compatible Lie algebras are given.

This https://arxiv.org/abs/2506.02885 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

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.

Gauge-invariant action for free string field theory with boundary
Carlo Maccaferri, Alberto Ruffino, Jakub Vo\v{s}mera
https://arxiv.org/abs/2506.05969 htt…

Gauge-invariant action for free string field theory with boundary
We construct fully gauge-invariant kinetic terms for open and closed string field theories on a target space with boundary. This is realized by promoting the gauge parameters at the boundary to extra dynamical modes describing boundary degrees of freedom. Having a gauge-invariant classical action, we also construct the corresponding BV master action and show that the master equation is obeyed thanks to a peculiar nilpotent structure of the BV kinetic operator. From this general construction we …

On the structure of groups defined by Kim and Manturov
Carl-Fredrik Nyberg-Brodda, Takuya Sakasai, Yuuki Tadokoro, Kokoro Tanaka
https://arxiv.org/abs/2506.08050

On the structure of groups defined by Kim and Manturov
We study the structure of a series of groups $Γ_n^4$ defined by Kim and Manturov. We show that the groups are finite for all $n \ge 6$ and in fact they are 2-step nilpotent $2$-groups.

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…

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.

This https://arxiv.org/abs/2506.00952 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On the class-breadth conjecture
The class-breadth conjecture of Leedham-Green, Neumann and Wiegold states that for each $p$-group, $cl(G)\leq b(G) + 1$, where $cl(G)$, $b(G)$ denote the nilpotency class and the breadth of $G$. While several counter-examples to this conjecture have been found for $p = 2$, it is still open in general for $p > 2$. This article is dedicated to one simplified version of the conjecture for $p > 2$.

$F$-injectivity does not imply $F$-fullness in normal domains
Alessandro De Stefani, Thomas Polstra, Austyn Simpson
https://arxiv.org/abs/2506.00646 https:…

$F$-injectivity does not imply $F$-fullness in normal domains
We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are $F$-injective but not $F$-full. Along the way, we find examples of two-dimensional local geometrically normal domains which are $F$-injective but not $F$-anti-nilpotent. A crucial theme of our constructions is the behavior of $F$-injectivity along a purely inseparable finite base change.

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…

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.