Tootfinder

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard
https://arxiv.org/abs/2403.20270

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to the algebraic one. In this paper, we push this ideology much further, describing a broad class of properties that transfer through Mekler's construction. This technique subsumes many well-known results and opens avenues for many more. As a straightforwa…

This https://arxiv.org/abs/2111.11274 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ad-invariant metrics on nonnice nilpotent Lie algebras
We proved in previous work that all real nilpotent Lie algebras of dimension up to $10$ carrying an ad-invariant metric are nice. In this paper we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than $10$ and every nilpotency step greater than $2$. In the way of doing so, we introduce a method to construct Lie algebras with ad-invariant metrics called the single extension, as a parallel to …

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Blaise Boissonneau, Aris Papadopoulos, Pierre Touchard
https://arxiv.org/abs/2403.20270

Mekler's Construction and Murphy's Law for 2-Nilpotent Groups
Mekler's construction is a powerful technique for building purely algebraic structures from combinatorial ones. Its power lies in the fact that it allows various model-theoretic tameness properties of the combinatorial structure to transfer to the algebraic one. In this paper, we push this ideology much further, describing a broad class of properties that transfer through Mekler's construction. This technique subsumes many well-known results and opens avenues for many more. As a straightforwa…

p-Nilpotent maximal subgroups in finite groups
Antonio Beltr\'an, Changguo Shao
https://arxiv.org/abs/2402.18413 https://arxiv.or…

p-Nilpotent maximal subgroups in finite groups
Let $G$ be a finite group, $p$ a prime, and suppose that every maximal subgroup of $G$ is $p$-nilpotent or has prime index in $G$. We prove, relying in the Classification of Finite Simple Groups, that if $p$ is odd and $p\neq 5$, then $G$ is $p$-solvable, and the $p$-length of $G$ is at most $2$. For $p=5$, however, a group $G$ satisfying the same conditions need not be $5$-solvable, and in that case we show that $G/S_5(G)\cong{\rm PSL}_2(11)$, where $S_5(G)$ is the $5$-solvable radical of $G$.…

Interesting piece on the relationship of Iran to the Palestinian struggle, and its limits.
Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar https://newleftreview.org/sidecar/posts/rules-of-the-game?pc=1598

Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar
Iran versus Israel.

This https://arxiv.org/abs/2302.00145 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Controllability of discrete-time linear systems on solvable Lie groups
The objective of this paper is to study the controllability of discrete-time linear control systems in solvable Lie groups. In the special case of nilpotent Lie groups, a necessary and sufficient condition for controllability is established. Furthermore, the class of discrete-time linear systems in the two-dimensional affine Lie group is constructed and a condition for controllability of these systems is also stated.

This https://arxiv.org/abs/2310.11519 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

On some counterparts of Rickart $*$-algebras
In the present paper, we introduce and study counterparts of Rickart involutive algebras, i.e., almost inner Rickart algebras. We prove that a nilpotent associative algebra, which has no nilpotent elements with nonzero square roots, is an almost inner Rickart algebra. A nilpotent associative algebra, which has no nilpotent elements with a square root $b$ such that $b^3\neq 0$, is not an almost inner Rickart algebra if there exists a nonzero element $a$ such that $a^2\neq 0$. As a main result of…

A Proof of the Box Conjecture for Commuting Pairs of Matrices
J. Irving, T. Ko\v{s}ir, M. Mastnak
https://arxiv.org/abs/2403.18574 https://

A Proof of the Box Conjecture for Commuting Pairs of Matrices
We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by Iarrobino et al \cite{IKvSZ}. This describes the Jordan type of the dense orbit in the nilpotent commutator of a given nilpotent matrix. Our main tool is the Burge correspondence between the set of all partitions and a set of binary words \cite{Bur-1, Bur-2}. For connection with the algebraic and geometric setup of matrices and orbits we employ some of Shayman's results on invariant subspaces of a nilpotent …

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
Tong Zhou
https://arxiv.org/abs/2404.19210 https://arxiv.org/p…

Character Sheaves on Reductive Lie Algebras in Positive Characteristic
We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and only if it has nilpotent singular support and is quasi-admissible. We also present geometric proofs, in positive characteristic, of the equivalence between being admissible and being a character sheaf, and various characterisations of cuspidal sheaves, follow…

Interesting piece on the relationship of Iran to the Palestinian struggle, and its limits.
Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar https://newleftreview.org/sidecar/posts/rules-of-the-game?pc=1598

Eskandar Sadeghi-Boroujerdi, Rules of the Game — Sidecar
Iran versus Israel.