Tootfinder

On finitely generated left nilpotent braces
H. Meng, A. Ballester-Bolinches, L. A. Kurdachenko, V. P\'erez-Calabuig
https://arxiv.org/abs/2508.07883 https://

On finitely generated left nilpotent braces
A description of finitely generated left nilpotent braces of class at most two is presented in this paper. The description heavily depends on the fact that if $B$ is left nilpotent of class at most $2$, that is $B^3 = 0$, then $B$ is right nilpotent of class at most $3$, that is $B^{(4)} = 0$. In addition, we construct a free object in the category of finitely generated left nilpotent braces of class at most $2$.

Bigraded Lie algebras and nilpotent fundamental groups of smooth complex algebraic varieties
Taito Shimoji
https://arxiv.org/abs/2510.09026 https://arxiv.o…

Bigraded Lie algebras and nilpotent fundamental groups of smooth complex algebraic varieties
Let $X$ be a smooth complex algebraic variety. Assume that the fundamental group $π_1(X,x)$ is torsion-free nilpotent. We show that if the betti number $b_1(X)$ is less than or equal to $3$, then $π_1(X,x)$ is isomorphic to $\mathbb{Z}$, $\mathbb{Z}^2$, $\mathbb{Z}^3$, a lattice in the Heisenberg group $H_3(\mathbb{R})$ or $\mathbb{R}\times H_3(\mathbb{R})$. Moreover we show that $π_1(X,x)$ is abelian or $2$-step nilpotent if the rank of $π_1(X,x)$ is less than or equal to seven. We prove t…

ConPoSe: LLM-Guided Contact Point Selection for Scalable Cooperative Object Pushing
Noah Steinkr\"uger, Nisarga Nilavadi, Wolfram Burgard, Tanja Katharina Kaiser
https://arxiv.org/abs/2510.08705

ConPoSe: LLM-Guided Contact Point Selection for Scalable Cooperative Object Pushing
Object transportation in cluttered environments is a fundamental task in various domains, including domestic service and warehouse logistics. In cooperative object transport, multiple robots must coordinate to move objects that are too large for a single robot. One transport strategy is pushing, which only requires simple robots. However, careful selection of robot-object contact points is necessary to push the object along a preplanned path. Although this selection can be solved analytically, …

Complex structures on two-step nilpotent Lie groups
Maria Laura Barberis
https://arxiv.org/abs/2508.05885 https://arxiv.org/pdf/2508.05885

Complex structures on two-step nilpotent Lie groups
We give a characterization of the $2$-step nilpotent Lie algebras whose corresponding Lie groups admit a left invariant complex structure. This is done by considering separately the cases when the complex structure is 2-step or 3-step nilpotent in the sense of [Cordero-Fernández-Gray-Ugarte, 2000]. We also study the Hermitian geometry 2-step nilpotent Lie groups. We show that if a left invariant Hermitian metric on such Lie group is pluriclosed, then the corresponding complex structure is 2-st…

Modular analogs of character formulas and multiplicities of induced representations
Patrick Allen, Preston Wake, Robin Zhang
https://arxiv.org/abs/2508.06657 https://

Modular analogs of character formulas and multiplicities of induced representations
Let $G$ be a finite group, $k$ a characteristic-$p$ field, and $π$ be a simple $k[G]$-module. We show that if $π$ is in a $p$-nilpotent block with cyclic defect group, then $π$ appears with multiplicity at most one in the socle and cosocle of induced $k[G]$-modules that are multiplicity-free in characteristic zero and satisfy some additional hypotheses. We show that this applies, in particular, to certain Deligne--Lusztig modules $π$. As an application, we prove that well-known character fo…

Crosslisted article(s) found for math.OA. https://arxiv.org/list/math.OA/new
[1/1]:
- Spectral and Nilpotent Matrix Orderings: Comparison and Applications in Dynamic Systems
Shih-Yu Chang

Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
Adri\'an Andrada, Mar\'ia Laura Barberis, Beatrice Brienza
https://arxiv.org/abs/2508.07889 https://…

Holonomy of the Obata connection on 2-step hypercomplex nilmanifolds
We study the holonomy of the Obata connection on 2-step hypercomplex nilmanifolds. By explicitly computing the curvature tensor, we determine the conditions under which the Obata connection is flat, showing that this depends on the nilpotency step of each complex structure. In particular, we show that the holonomy algebra of the Obata connection is always an abelian subalgebra of $\mathfrak{sl}(n, \mathbb{H})$: to establish this, we prove the $\mathbb{H}$-solvable conjecture for 2-step hypercom…

Homogeneous locally nilpotent derivations on trinomial varieties
Kirill Rassolov
https://arxiv.org/abs/2509.08491 https://arxiv.org/pdf/2509.08491

Homogeneous locally nilpotent derivations on trinomial varieties
We consider the finest grading of the algebra of regular functions of a trinomial variety. An explicit description of locally nilpotent derivations that are homogeneous with respect to this grading is obtained.

Replaced article(s) found for math.RT. https://arxiv.org/list/math.RT/new
[1/1]:
- Stable distributions and nilpotent orbital integrals
Jean-Loup Waldspurger (IMJ-PRG)

Period maps at infinity
Mark Green, Phillip Griffiths, Colleen Robles
https://arxiv.org/abs/2509.08508 https://arxiv.org/pdf/2509.08508

Period maps at infinity
Let $\overline{B}$ be a smooth projective varieity, and $Z \subset \overline{B}$ a simple normal crossing divisor. Assume that $B = \overline{B} - Z$ admits a variation of pure, polarized Hodge structure. The divisor $Z$ is naturally stratified, and Schmid's nilpotent orbit theorem defines a family/variation of nilpotent orbits along each strata. We study the rich geometric structure encoded by this family, its relationship to the induced (quotient) variation of pure Hodge structure on the stra…