A Hecke symmetry on a finite dimensional vector space gives rise to two graded factor algebras and of the tensor algebra of which are regarded as quantum analogs of the symmetric and the exterior algebras. Another graded algebra associated with is the Faddeev–Reshetikhin–Takhtajan bialgebra which coacts on and . There are also more general graded algebras defined with respect to pairs of Hecke symmetries and interpreted in terms of quantum hom-spaces. Their nice behaviour has been known under the assumption that the parameter of the Hecke relation is such that for all . The present paper makes an attempt to investigate several questions without this condition on . Particularly we are interested in Koszulness and Gorensteinness of those graded algebras. For a root of 1 positive results require a restriction on the indecomposable modules for the Hecke algebras of type that can occur as direct summands of representations in the tensor powers of .
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Serge Skryabin, On the graded algebras associated with Hecke symmetries. J. Noncommut. Geom. 14 (2020), no. 3, pp. 937–986DOI 10.4171/JNCG/383