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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The homological determinant of quantum groups of type $A$


Author: Phùng Hô Hai
Journal: Proc. Amer. Math. Soc. 133 (2005), 1897-1905
MSC (2000): Primary 16W30, 17B37; Secondary 17A45, 17A70
Published electronically: February 15, 2005
MathSciNet review: 2137853
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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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Additional Information

Phùng Hô Hai
Affiliation: Institute of Mathematics, P.O. Box 631, 10000 Boho, Hanoi, Vietnam
Address at time of publication: FB6 Mathematik, Universität Duisburg–Essen, 45117 Essen, Germany
Email: phung@math.ac.vn, ho-hai.phung@uni-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07739-7
PII: S 0002-9939(05)07739-7
Received by editor(s): September 19, 2002
Received by editor(s) in revised form: February 22, 2004
Published electronically: February 15, 2005
Additional Notes: This work was supported by the National Program of Basic Sciences Research of Vietnam
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society