Silting mutation in triangulated categories (1009.3370v3)

Abstract: In representation theory of algebras the notion of mutation' often plays important roles, and two cases are well known, i.e.cluster tilting mutation' and exceptional mutation'. In this paper we focus ontilting mutation', which has a disadvantage that it is often impossible, i.e. some of summands of a tilting object can not be replaced to get a new tilting object. The aim of this paper is to take away this disadvantage by introducing silting mutation' for silting objects as a generalization oftilting mutation'. We shall develope a basic theory of silting mutation. In particular, we introduce a partial order on the set of silting objects and establish the relationship with `silting mutation' by generalizing the theory of Riedtmann-Schofield and Happel-Unger. We show that iterated silting mutation act transitively on the set of silting objects for local, hereditary or canonical algebras. Finally we give a bijection between silting subcategories and certain t-structures.