Open AccessThe homological determinant of quantum groups of type 𝐴
Author(s) -
Phùng Hô Hái
Publication year - 2005
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/s0002-9939-05-07739-7
Subject(s) - type (biology) , pure mathematics , quantum , mathematics , algebra over a field , physics , biology , quantum mechanics , ecology
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 .