讲座题目：Lie algebras arising from two-periodic projective complex and derived categories
主讲人：肖杰 教授
主持人：胡乃红 教授
开始时间：2024-05-24 10:00
讲座地址：闵行校区数学楼401报告厅
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：
Let A be a finite-dimensional C-algebra of finite global dimension and consider the category of finitely 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.
