# The homological determinant of quatum groups of type A

@article{Hai2003TheHD, title={The homological determinant of quatum groups of type A}, author={Ph{\`u}ng Hồ Hai}, journal={arXiv: Quantum Algebra}, year={2003} }

A quantum group of type A is defined as a Hopf algebra associated to a Hecke symmetry. We show the homology of a Koszul complex associated to the Hecke symmetry is one dimensional and determines a group-like element in the Hopf algebra. This group-like element can be interpreted as a homological determinant as suggested by Yu. Manin.

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