On the graded algebras associated with Hecke symmetries

2019/03/15 by Skryabin, Serge
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1903.06363

Abstract

We consider quantum symmetric algebras, FRT bialgebras and, more generally, intertwining algebras for pairs of Hecke symmetries which represent quantum hom-spaces. The paper makes an attempt to investigate Koszulness and Gorensteinness of those graded algebras without a restriction on the parameter q of the Hecke relation used earlier. When q is a root of 1, positive results require a restriction on the indecomposable modules for the Hecke algebras of type A that can occur as direct summands of representations in the tensor powers of the base space.

Related

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• Realizations of quantum hom-spaces, invariant theory and quantum determinantal ideals
• A new approach to the Koszul property in representation theory using graded subalgebras
• Schur algebras and quantum symmetric pairs with unequal parameters