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Contractibility of the stability manifold for silting-discrete algebras

Banff International Research Station for Mathematical Innovation and Discovery

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.

Mathematics; Algebraic geometry; Associative rings and algebras; Representation theory

video/mp4

Author affiliation: Universität Stuttgart

2019-05-01

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/70012

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/