中科院数学与系统科学研究院
数学研究所
学术报告
表示论研讨班
报告人：陈红星 教授（首都师范大学）
题 目：Homological theory of mirror symmetric algebras
时 间：2022.04.19（星期二），16:00-17:00
地 点：腾讯会议 894-927-420
摘 要：Given an algebra with an idempotent, we first introduce a mirror symmetric algebra and its deformations via central elements, and then provide some basic properties of mirror symmetric algebras. As an application, we show that Tachikawa’s second conjecture holds for all symmetric algebras if and only if all indecomposable symmetric algebras have no nonzero strong idempotent ideals. It turns out that if all indecomposable symmetric algebras are derived simple, then Tachikawa’s second conjecture holds for all symmetric algebras. Recall that the conjecture predicts that a finitely generated, orthogonal module over a finite-dimensional self-injective algebra is projective.
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