Symmetric subcategories and good tilting modules

Tilting modules have played an important role in representation theory of algebras. Especially, infinitely generated tilting modules provide completely different features. In this case, recollements of triangulated categories in the sense of Beilinson-Bernstein-Deligne enter into the play. In this talk, we introduce symmetric subcategories and show that, for any good tilting module over an algebra, the derived category of the endomorphism algebra of the tilting module is always a recollement of the derived categories of the given algebra and a symmetric subcategory of a module category. Explicit examples of symmetric subcategories associated to 2-good tilting modules over commutative Gorenstein rings are presented. This talk reports a joint work with Hongxing Chen.