Tootfinder

This https://arxiv.org/abs/2206.05906 has been replaced.
link: https://scholar.google.com/scholar?q=a

A note on homogeneous rank $2$ locally nilpotent derivations on $k[X,Y,Z]$
In this article we show that for every prime number $p$, any irreducible homogeneous locally nilpotent derivations of rank $2$ and degree $p-2$ are triangularizable. Further, we describe the structure of irreducible non-triangularizable homogeneous locally nilpotent derivations of rank $2$ and degree $pq-2$, where $p,q$ are prime numbers. Consequently, we give explicit descriptions of the generators of the image ideals of certain homogeneous locally nilpotent derivations of rank $2$.

On Commuting automorphisms of nilpotent Lie algebras
Shushma Rani, Niranjan Nehra, Rohit Garg
https://arxiv.org/abs/2404.12998 https://

On Commuting automorphisms of nilpotent Lie algebras
We investigate the commuting automorphisms of nilpotent Lie algebras $L$ with coclass $\leq 3$. Our examination exposes the conditions under which the set of commuting automorphisms of $L$ forms a subgroup within its automorphism group.

This https://arxiv.org/abs/2311.08208 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Modular Representations of Truncated current Lie algebras
In this paper we consider the structure and representation theory of truncated current algebras $\mathfrak{g}_m = \mathfrak{g}[t]/(t^{m+1})$ associated to the Lie algebra $\mathfrak{g}$ of a standard reductive group over a field of positive characteristic. We classify semisimple and nilpotent elements and describe their associated support varieties. Next, we prove various Morita equivalences for reduced enveloping algebras, including a reduction to nilpotent $p$-characters, analogous to a famou…

When the lesser of two evils isn't
https://newleftreview.org/issues/ii145/articles/lorna-finlayson-on-lesser-evilism-37ead90d-ae94-43ce-a171-3d0f3ad3e9ca

Lorna Finlayson, On Lesser Evilism, NLR 145, January–February 2024
The standard argument for backing hawkish centre-left parties remains the ‘lesser evil’. Lorna Finlayson interrogates that line of reasoning and the assumptions on which it rests: crude consequentialism, narrow minded electoralism and covering up the realities of Starmer’s Labour.

This https://arxiv.org/abs/2403.09423 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A survey on conjugacy class graphs of groups
There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider commuting/nilpotent/solvable conjugacy class graph of $G$ where two distinct conjugacy classes $a^G$ and $b^G$ are adjacent if there exist some elements $x\in a^G$ and $y\in b^G$ such that $\langle x, y \rangle$ is abelian/nilpotent/solvable. After a section of …

Cutoff for random Cayley graphs of nilpotent groups
Jonathan Hermon, Xiangying Huang
https://arxiv.org/abs/2403.12355 https://arxiv.o…

Cutoff for random Cayley graphs of nilpotent groups
We consider the random Cayley graphs of a sequence of finite nilpotent groups of diverging sizes $G=G(n)$, whose ranks and nilpotency classes are uniformly bounded. For some $k=k(n)$ such that $1\ll\log k \ll \log |G|$, we pick a random set of generators $S=S(n)$ by sampling $k$ elements $Z_1,\ldots,Z_k$ from $G$ uniformly at random with replacement, and set $S:=\{Z_j^{\pm 1}:1 \le j\le k \}$. We show that the simple random walk on Cay$(G,S)$ exhibits cutoff with high probability. S…

Moduli spaces of nilpotent displays
Sebastian Bartling, Manuel Hoff
https://arxiv.org/abs/2404.10132 https://arxiv.org/pdf/2404.10132…

Moduli spaces of nilpotent displays
We show that the moduli problem of deformations of nilpotent displays by quasi-isogenies is representable, without using $p$-divisible groups. The main ingredients are Artin's criterion and the theory of truncated displays. This gives in particular a new proof for the representability of Rapoport-Zink spaces.

This https://arxiv.org/abs/2202.12630 has been replaced.
link: https://scholar.google.com/scholar?q=a

Some results on homogeneous locally nilpotent $R$-derivations on $R[X,Y,Z]$
Let $k$ be a field of characteristic zero and $R$ a $k$-algebra. In this paper we study homogeneous $R$-lnds $D$ on $R[X,Y,Z]$ with respect to the standard weights $(1,1,1)$. We show that when $R$ is a PID, $rank(D)$ can be at most $2$ if $°(D) \leqslant 3$. As a consequence we obtain a certain class of homogeneous lnds on $k^{[4]}$ whose kernel is $k^{[3]}$. Further when $R$ is a Dedekind domain, we give a bound for minimum number of generators of $\ker(D)$ as an $R$-algebra if $°(D) \leqsla…

This https://arxiv.org/abs/2403.09423 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

A survey on conjugacy class graphs of groups
There are several graphs defined on groups. Among them we consider graphs whose vertex set consists conjugacy classes of a group $G$ and adjacency is defined by properties of the elements of conjugacy classes. In particular, we consider commuting/nilpotent/solvable conjugacy class graph of $G$ where two distinct conjugacy classes $a^G$ and $b^G$ are adjacent if there exist some elements $x\in a^G$ and $y\in b^G$ such that $\langle x, y \rangle$ is abelian/nilpotent/solvable. After a section of …

Nilpotent symplectic alternating algebras II
Layla Sorkatti, Gunnar Traustason
https://arxiv.org/abs/2404.11038 https://arxiv.org/pdf…

Nilpotent symplectic alternating algebras II
In this paper and its sequel we continue our study of nilpotent symplectic alternating algebras. In particular we give a full classification of such algebras of dimension $10$ over any field. It is known that symplectic alternating algebras over $\mbox{GF}(3)$ correspond to a special rich class $\mathcal{C}$ of $2$-Engel $3$-groups of exponent $27$ and under this correspondence we will see that the nilpotent algebras correspond to a subclass of $\mathcal{C}$ that are those groups in $\mathcal{C…