Tootfinder

The prescribed Ricci curvature problem on 5-dimensional nilpotent Lie groups
Marius Landry Foka, Romain Pefoukeu Nimpa, Salomon Joseph Mbatakou, Michel Bertrand Ngaha Djiadeu, Thomas Bouetou Bouetou
https://arxiv.org/abs/2403.08402

The prescribed Ricci curvature problem on 5-dimensional nilpotent Lie groups
In this paper, using the Milnor-type theorem technique, we provide on each nilpotent five dimensional Lie group, some global existence result of a pair (g, c) consisting of a left-invariant Riemannian metric g and a positive constant c such that Ric(g) =cT, where Ric(g) is the Ricci curvature of g and T a given left-invariant symmetric (0, 2)-tensor field.

This https://arxiv.org/abs/2402.04053 has been replaced.
link: https://scholar.google.com/scholar?q=a

Ramification filtration via deformations, II
Let $\mathcal K$ be a field of formal Laurent series with coefficients in a finite field of characteristic $p$. For $M\in\mathbb{N}$, let $\mathcal G_{

This https://arxiv.org/abs/2212.07930 has been replaced.
link: https://scholar.google.com/scholar?q=a

Singular contact varieties
In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational singularities and prove basic properties of such objects. Natural examples of singular contact varieties come from the theory of nilpotent orbits: every projectivization of the closure of a nilpotent orbit in a semisimple Lie algebra satisfies our definition after normalization. We show the correspondence between symplectic varieties with the stru…

This https://arxiv.org/abs/2104.04754 has been replaced.
link: https://scholar.google.com/scholar?q=a

Forbidden subgraphs in enhanced power graphs of finite groups
The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal grap…

A survey on conjugacy class graphs of groups
P. J. Cameron, F. E. Jannat, R. K. Nath, R. Sharafdini
https://arxiv.org/abs/2403.09423 https://

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 …

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…

Towards a Stallings-type theorem for finite groups
Johannes Carmesin, George Kontogeorgiou, Jan Kurkofka, Will J. Turner
https://arxiv.org/abs/2403.07776 h…

Towards a Stallings-type theorem for finite groups
A recent development in graph theory is to study local separators, vertex sets that need not separate graphs globally but just locally. We use this idea to conjecture an extension of Stallings' theorem to finite nilpotent groups. We provide an example demonstrating that the assumption of nilpotency is necessary, and prove a stronger form of this conjecture for low connectivities, as follows. A finite nilpotent group that has a Cayley graph with a local separator of size at most two is cyclic,…

Real Nullstellensatz for 2-step nilpotent Lie algebras
Philipp Schmitt, Matthias Sch\"otz
https://arxiv.org/abs/2403.06773 https://

Real Nullstellensatz for 2-step nilpotent Lie algebras
We prove a noncommutative real Nullstellensatz for 2-step nilpotent Lie algebras that extends the classical, commutative real Nullstellensatz as follows: Instead of the real polynomial algebra $\mathbb R[x_1, \dots, x_d]$ we consider the universal enveloping *-algebra of a 2-step nilpotent real Lie algebra (i.e. the universal enveloping algebra of its complexification with the canonical *-involution). Evaluation at points of $\mathbb R^d$ is then generalized to evaluation through integrable *-r…

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…

Regular nilpotent partial Hessenberg varieties
Tatsuya Horiguchi
https://arxiv.org/abs/2405.07247 https://arxiv.org/pdf/2405.07247