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Quantum double finite group algebras and their representations

Published online by Cambridge University Press:  17 April 2009

M.D. Gould
M.D. Gould
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
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The quantum double construction is applied to the group algebra of a finite group. Such algebras are shown to be semi-simple and a complete theory of characters is developed. The irreducible matrix representations are classified and applied to the explicit construction of R-matrices: this affords solutions to the Yang-Baxter equation associated with certain induced representations of a finite group. These results are applied in the second paper of the series to construct unitary representations of the Braid group and corresponding link polynomials.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 2 , October 1993 , pp. 275 - 301
Copyright
Copyright © Australian Mathematical Society 1993

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