The homological determinant of quantum groups of type 𝐴

Hai, Phùng

doi:10.1090/S0002-9939-05-07739-7

The homological determinant of quantum groups of type $A$
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by Phùng Hồ Hai PDF

Proc. Amer. Math. Soc. 133 (2005), 1897-1905 Request permission

Abstract:

Let $R$ be a Hecke symmetry depending algebraically on a parameter $q\in \mathbb {C}$. We show that the homology of the Koszul complex associated with $R$ is one-dimensional when $q$ is not a root of unity. A generator of this homology group then induces the homological determinant of the quantum group associated with $R$.

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