Speaker：Xin Liu（Chinese Academy of Sciences）

Time：2022-11-17, 16:30

Location：Tencent Meeting ID：141-760-228（No Password）

Abstract:

In the general context of tilting theory, a central theme is to study relations between the derived module categories of the given algebras and the endomorphism algebras of tilting modules. In the talk, we introduce symmetric subcategories and show that for any good tilting module T over an algebra A, the derived category of the endomorphism algebra B of T is a recollement of the derived categories of A and a symmetric subcategory of the module category of B, in the sense of Beilinson-Bernstein-Deligne. Thus the kernel of the total left-derived tensor functor induced by a good tilting module is always triangle equivalent to the derived category of a symmetric subcategory of a module category. Explicit description of symmetric subcategories associated to a class of good 2-tilting modules over commutative Gorenstein local rings are presented. This is joint work with Changchang Xi