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SUMMARY:Tiago Cruz (Universität Stuttgart)
DTSTART:20220523T130000Z
DTEND:20220523T140000Z
DTSTAMP:20260423T021328Z
UID:GANT/12
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GANT/12/">Ri
 ngel self-duality via relative dominant dimension</a>\nby Tiago Cruz (Univ
 ersität Stuttgart) as part of Greek Algebra & Number Theory Seminar\n\n\n
 Abstract\nQuasi-hereditary algebras provide an abstract framework for the 
 homological structure of Schur algebras and the BGG category $O$ of a semi
 -simple Lie algebra and they always appear in pairs via Ringel duality.\n\
 nIn this talk\, we discuss a generalisation of dominant dimension using re
 lative homological algebra. This homological invariant is compatible with 
 the tools from integral representation theory and it increases our underst
 anding of classical dominant dimension.\n\nIn particular\, this homologica
 l invariant provides tools to deduce that quasi-hereditary covers formed b
 y quasi-hereditary algebras with a simple preserving duality with large en
 ough dominant dimension also appear in pairs. As an application\, we give 
 a new proof of Ringel self-duality of the blocks of the BGG category $O$ o
 f a complex semi-simple Lie algebra.\n
LOCATION:https://researchseminars.org/talk/GANT/12/
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