Séminaires : Séminaire d'Algèbre

This work is an attempt to understand the maximal natural generality context for the Koenig-Kuelshammer-Ovsienko construction in the theory of quasi-hereditary algebras by putting it into a category-theoretic context. Given a field k and a k-linear exact category E with a chosen set of nonzero objects F_i such that every object of E is a finitely iterated extension of some F_i, we construct a coalgebra C whose irreducible comodules 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 the nontrivial homomorphisms between the chosen objects F_i in E while keeping the Ext spaces unchanged. The removed homomorphisms are then repackaged into a semialgebra S over C such that the exact category E can be recovered as the category of S-semimodules induced from finite-dimensional C-comodules. The construction used Koszul duality twice: once as absolute and once as relative Koszul duality.
 

Talk shared by the GAP conference, cf. https://personal.psu.edu/mps16/hirsutes2023/gap2023.html

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