報告時間：2024年06月20日（星期四）9:30
報告地點：翡翠湖校區科教樓B座1710室
報 告 人：尚士魁 副教授
工作單位：上海大學
舉辦單位：數學學院
報告簡介：
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.
報告人簡介：
尚士魁，上海大學副教授，畢業于中國科學技術大學。后在中科院信工所作特聘研究員，主要研究興趣量子群、量子計算，后量子密碼等。報告人已在J. Algebra, Contemp. Math., Comm. Algebra等發表論文多篇。曾多次擔任全國大學生數學密碼挑戰賽出題專家和評審專家。
