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建党100周年70周年校庆卓越育人学术育人不言之教幸福之花

5月24日 肖杰:Lie algebras arising from two-periodic projective complex and derived categories(知名学者系列学术报告)
2024-05-24 10:00:00
活动主题:Lie algebras arising from two-periodic projective complex and derived categories
主讲人:肖杰
开始时间:2024-05-24 10:00:00
举行地点:闵行校区数学楼报告厅401
主办单位:数学科学学院

报告人简介:肖杰,北京师范大学数学科学学院教授、博士生导师。曾获得国家杰出青年基金、教育部跨世纪人才基金,教育部自然科学一等奖等。曾担任中国科学、数学学报、数学年刊、Algebra Colloquium等编委,Pure and Applied Mathematics  Quarterly 副主编,中国数学会常务理事。2006年至2017年任清华大学数学科学系主任,2014年至2017年任清华大学理学院院长。主要从事代数表示论与量子群的交叉研究。在代数表示论、Ringel-Hall代数、量子群和范畴化等领域做出了一系列重要科研成果。相关研究成果发表于Invent. Math., Duke Math. J.,  Compositio Math., Adv. Math., Math. Z.等重要学术期刊。

报告内容介绍:Let A be a ?nite-dimensional C-algebra of ?nite global dimension and consider the category of  ?nitely generated right A-modules. By using of the category of two-periodic projective  complexes C2(P), we construct the motivic Bridgeland’s Hall algebra for A, where structure  constants are given by Poincaré polynomials in t, then construct a C-Lie subalgebra g = n⊕h at  t = ?1, where n is constructed by stack functions about indecomposable radical complexes, and  h is by contractible complexes. For the stable category K2(P) of C2(P), we construct its moduli  spaces and a C-Lie algebra ?g = ?n⊕?h, where ?n is constructed by support-indecomposable  constructible functions, and ?h is by the Grothendieck group of K2(P). We prove that the natural  functor C2(P) → K2(P) together with the natural isomorphism between Grothendieck groups  of A and K2(P) induces a Lie algebra isomorphism g ~ = ?g. This makes clear that the structure  constants at t = ?1 provided by Bridgeland in [5] in terms of exact structure of C2(P) precisely  equal to that given in [30] in terms of triangulated category structure of K2(P). This is based on  the joint work with J. Fang and Y. Lan.

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