The relationship between skew group algebras and orbifold theory

PBW deformations of skew polynomial rings and their group extensions

We examine PBW deformations of finite group extensions of skew polynomial rings, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

A Z_2-orbifold model of the symplectic fermionic vertex operator superalgebra

We construct an irrational C_2-cofinite vertex operator algebra associatted to a finite dimensional vector space with a nondegenerate skew-symmetric bilinear form. We also classify its equivalence classes of irreducible modules and determine its automorphism group.

A remark on ${\mathbb Z}_p$-orbifold constructions of the Moonshine vertex operator algebra

For $p = 3,5,7,13$, we consider a ${\mathbb Z}_p$-orbifold construction of the Moonshine vertex operator algebra $V^\natural$. We show that the vertex operator algebra obtained by the ${\mathbb Z}_p$-orbifold construction on the Leech lattice vertex operator algebra $V_Λ$ and a lift of a fixed-point-free isometry of order $p$ is isomorphic to the Moonshine vertex operator algebra $V^\natural$. We also describe the relationship between those ${\mathbb Z}_p$-orbifold constructions and the ${\mathbb Z}_2$-orbifold construction in a uniform manner. In Appendix, we give a characterization of the Mo…

斜左括号与三因子化群的范畴

Categories of skew left braces and trifactorised groups

本文旨在深化斜左括号与三因子化群之间的联系，该联系编码了斜左括号的结构、商及同态信息。

斜 brace 中的下中心列和上中心列的类似物：综述

Analogs of the lower and upper central series in skew braces: a survey

本文综述斜 brace 的左列、右列等类似群下/上中心列的结构，证明其项间关系的新结果，探讨 Bonatto 和 Jedlička 定义的斜 brace 下中心列及 Ballester - Bolinches 等人提出的理想下中心列概念。