报告时间：2024年06月20日（星期四）上午：9：30-10:30

报告地点：翡翠科教楼B1710

报告人： 尚士魁 副教授

工作地点：上海大学

举办单位：数学学院

报告摘要：

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。