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SUMMARY:Leonid Positselski (Prague)
DTSTART:20230522T121500Z
DTEND:20230522T131500Z
DTSTAMP:20260710T044504Z
UID:paris-algebra-seminar/133
DESCRIPTION:Title: The homomorphism removal and repackaging construction\
nby Leonid Positselski (Prague) as part of Paris algebra seminar\n\n\nAbst
ract\nThis work is an attempt to understand the maximal natural generality
context for\nthe Koenig-Kuelshammer-Ovsienko construction in the theory o
f quasi-hereditary algebras by\nputting it into a category-theoretic conte
xt. Given a field k and a k-linear exact category E \nwith a chosen set of
nonzero objects F_i such that every object of E is a finitely iterated \n
extension of some F_i\, we construct a coalgebra C whose irreducible comod
ules L_i are indexed by the same indexing set\, and an exact functor from
C-comod to E taking L_i to F_i such that the spaces Ext^n between L_i in C
−comod are the same as between F_i in E (for n > 0). Thus\, the abelian
category C−comod is obtained from the exact category E by removing all t
he nontrivial homomorphisms between the chosen objects F_i in E while keep
ing the Ext spaces unchanged. The removed homomorphisms are then repackage
d into a semialgebra S over C such that the exact category E can be recove
red as the category of S-semimodules induced from finite-dimensional C-com
odules. The construction used Koszul duality twice: once as absolute and o
nce as relative Koszul duality.\n\n\nThis talk will take place in hybrid f
ormat at the GAP conference at the Institut Henri Poincaré\, cf. GAP.\n
LOCATION:https://researchseminars.org/talk/paris-algebra-seminar/133/
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