BIRS Workshop Lecture Videos
Contractibility of the stability manifold for silting-discrete algebras Zvonareva, Alexandra
For bounded derived categories of finite-dimensional algebras, due to the bijection of Koenig and Yang, silting objects correspond to t-structures whose hearts are equivalent to module categories of finite-dimensional algebras. Silting-discrete algebras are algebras which have only finitely many silting objects in any interval in the poset of silting objects. Examples of silting discrete algebras include hereditary algebras of finite representation type, derived-discrete algebras, symmetric algebras of finite representation type and many others. I will explain that any bounded t-structure in the bounded derived category of a silting-discrete algebra is algebraic, i.e. its heart is equivalent to a module category of a finite-dimensional algebra. As a corollary, the space of Bridgeland stability conditions for a silting-discrete algebra is contractible.
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