汇报标题 (Title)：New invariants of stable equivalences and Alperin–Auslander conjecture
（不变等价的新不变量与Alperin-Auslander猜测）
汇报人 (Speaker)：惠昌常 教授（首都师范大学）
汇报功夫 (Time)：2026年5月7日（周四）14:30
汇报地址 (Place)：校本部F309
约请人(Inviter)：张红莲教授
主办部门：理学院数学系
汇报提要：The not yet solved Alperin–Auslander/Auslander–Reiten conjec
ture, in the representation theory of algebras and groups, states that the
number of non-isomorphic, non-projective simple modules of an algebra is
invariant under stable equivalences of algebras. In this talk, we show that
the conjecture is valid for two classes of algebras: the centralizer matrix
algebras and Frobenius-finite algebras. Moreover, we show some new ho
mological invariants of stable equivalences of algebras. The talk reports
parts of a joint work with Jinbi Zhang in Math. Ann. 394(4)(2026).
