On stable equivalences of algebras

发布时间：2024-03-15 作者：浏览次数：

Speaker:	惠昌常教授	DateTime:	2024年03月22日（周五）8：30-9：15
Brief Introduction to Speaker: 惠昌常，首都师范大学特聘教授，博士生导师，CJXZ特聘教授；曾获教育部科技进步二等奖、德国“年轻杰出学者洪堡奖”；在代数表示论、同调代数、导出范畴、代数K-理论等学科取得了出色的研究成果, 在Adv. in Math., J. Reine Angew. Math., Proc. Lond. Math. Soc., Trans. Amer. Math. Soc., Math. Ann., Comm. Math. Phys., Sci. China Math. 等国际数学刊物发表论文90多篇，多次在国际代数学术会议作大会报告、主持和参加国家自然科学基金重点项目；任《Journal of Algebra》、《Archiv der Mathematik》等国际数学杂志编委。		Place:	六号楼二楼报告厅
Abstract:In the representation theory of algebras and groups, one of the major conjectures is the long-standing and not yet solved Auslander-Reiten/Auslander-Alperin conjecture on stable equivalences, stating that the numbers of non-isomorphic, non-projective simple modules of algebras are invariant under stable equivalences. In this talk, we will show that self-injectivity of algebras over a field is invariant of stable equivalences. This completes a proof of a result of Rickard and Rouquier. Also, we present new invariants of stable equivalences of Artin algebras and show that the conjecture holds true for centralizer algebras of matrices. The talk reports some results jointly with Jin Zhang, and with Jinbi Zhang.

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