学术交流
位置: 首页 > 学术交流 > 正文

尚士魁: Free nonunital alternative algebras and ABG construction

时间:2024-06-19来源:数学学院

报告时间20240620日(星期四)9:30

报告地点翡翠湖校区科教楼B1710室

:尚士魁 副教授

工作单位上海大学

举办单位:数学学院

报告简介

Let $k$ be a field of characteristic $0$. We introduce a pair of adjoint functors, Allison-Benkart-Gao functor $\AG$ and Berman-Moody functor $\BM$, between the category of non-unital alternative algebras over $k$ and the category $\LieR$ of Lie algebras with appropriate $sl_3(k)$-module structures. Surprisingly, when $A$ is a non-unital alternative algebra, the Allison-Benkart-Gao Lie algebra $\AG(A)$ is different from the more well-known Steinberg Lie algebra $st_3(A)$.

Next, let $A(D)$ be the free (non-unit) alternative algebra generated by $D$ elements and $\innAD$ the inner derivation algebra of $A(D)$.  A conjecture on the homology of $H_r(\AGAD)$ is proposed.

Let $A(D)_n$(resp. $\innAD_n$) be the degree $n$ component of $A(D)_n$(resp. $\innAD_n$). The previous conjecture implies another conjecture on the dimensions on $A(D)_n$ and $\text{Inner} A(D)_n$. We also give some evidences to support the these conjectures.

报告人简介

尚士魁,上海大学副教授,毕业于中国科学技术大学。后在中科院信工所作特聘研究员,主要研究兴趣量子群、量子计算,后量子密码等。报告人已在J. Algebra, Contemp. Math., Comm. Algebra等发表论文多篇。曾多次担任全国大学生数学密码挑战赛出题专家和评审专家

关闭

Baidu
sogou