The homological determinant of quantum groups of type 𝐴

Abstract

Let R R be a Hecke symmetry depending algebraically on a parameter q ∈ C q\in \mathbb {C} . We show that the homology of the Koszul complex associated with R R is one-dimensional when q 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 R .