Gendo-Frobenius algebras and comultiplication

量子完全交上的双Frobenius代数结构

Bi-Frobenius algebra structure on quantum complete intersections

本文在量子完全交上构造双Frobenius代数结构，给出参数条件并证明其非双代数性，同时探讨量子外代数的相应结构。

Frobenius Heisenberg 范畴的基础

Foundations of Frobenius Heisenberg categories

本文研究 Frobenius Heisenberg 范畴的态射空间基，利用范畴余乘法与广义分圆商证明相关猜想，并表明其 Karoubi 包络的 Grothendieck 环恢复对应格 Heisenberg 代数。

双代数的扭曲张量积与Frobenius代数之间的二分性

A dichotomy between twisted tensor products of bialgebras and Frobenius algebras

该研究为扭曲张量积定义余单位与余乘法结构，刻画其成为余代数、双代数、Frobenius代数等的条件，方法适用于辫子幺半范畴，并得到相关代数构造应用。

Invariant algebras of matrices and symmetric polynomials of partitions

For a field $R$ of characteristic $p\ge 0$ and a matrix $c$ in the full $n\times n$ matrix algebra $M_n(R)$ over $R$, let $S_n(c,R)$ be the centralizer algebra of $c$ in $M_n(R)$. We show that $S_n(c,R)$ is a Frobenius-finite, $1$-Auslander-Gorenstein, and gendo-symmetric algebra, and that the extension $S_n(c,R)\subseteq M_n(R)$ is separable and Frobenius. Further, we study the isomorphism problem of invariant matrix algebras. Let $σ$ be a permutation in the symmetric group $Σ_n$ and $c_σ$ the corresponding permutation matrix in $M_n(R)$. We give sufficient and necessary conditions for the in…

On the algebra structure of some bismash products

We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product $H_q$ of dimension $q(q-1)(q+1)$ to each of the finite groups $PGL_2(q)$ and show that these $H_q$ do not have the structure (as algebras) of group algebras (except when $q =2,3$). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the st…