The homological determinant of quatum groups of type A

2003/05/08 by Phùng Hô Hái, Hai, Phung Ho
Mathematics · #16W30 #17A45 #17A70 #17B37 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.math/0305115

openalex publication_date 2003/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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