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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The homological determinant of quantum groups of type $A$
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by Phùng Hồ Hai PDF
Proc. Amer. Math. Soc. 133 (2005), 1897-1905 Request permission


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 Hồ 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:,
  • 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
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1897-1905
  • MSC (2000): Primary 16W30, 17B37; Secondary 17A45, 17A70
  • DOI:
  • MathSciNet review: 2137853