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- W3132832054 abstract "This thesis concerns Hall algebras. We define twisted extended Hall algebras of triangulated categories and show that in some cases they are well-defined even when their non-extended counterparts are not. We show that each exact category with weak equivalences with an appropriate extra structure naturally gives rise to a twisted extended Hall algebra of its homotopy category.We prove that this construction recovers Bridgeland's categorification of quantum groups via Hall algebras of complexes and its generalization due to Lu and Peng. We prove that the algebras thus defined are functorial under exact functors respecting weak equivalences. This allows us to prove the tilting invariance of Bridgeland's algebras and to categorify Lusztig's symmetries of quantum groups. Under suitable finiteness conditions, for two different exact structures on the same additive category with one having strictly less conflations than the other, we define a filtration on the Hall algebra of the latter whose associate graded is the Hall algebra of the former. This construction generalizes quantum PBW-type filtrations." @default.
- W3132832054 created "2021-03-01" @default.
- W3132832054 creator A5049743105 @default.
- W3132832054 date "2019-12-19" @default.
- W3132832054 modified "2023-09-23" @default.
- W3132832054 title "Hall algebras and localization of categories" @default.
- W3132832054 hasPublicationYear "2019" @default.
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