Quantum double finite group algebras and their representations

1993/10/01 by M.D. Gould, M. D. Gould · 7 citations
Mathematics · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Advanced Operator Algebra Research

paper · pdf · doi:10.1017/s0004972700015707

Abstract

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.

Cited by

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• Simple Yetter-Drinfeld modules over infinite-dimensional Taft algebras
• Partition function of the Kitaev quantum double model
• Pauli Stabilizer Models for Gapped Boundaries of Twisted Quantum Doubles and Applications to Composite Dimensional Codes
• Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of A_{N 2n+1}^μλ
• The Category of Anyon Sectors for Non-Abelian Quantum Double Models. [europepmc]

Related

• Lectures on Quantum Groups and Yang-Baxter Equations
• The l-State Boson Algebra as a Non-Standard Quantum Double and its Universal R-Matrix for Yang-Baxer Equation
• Solutions of quantum Yang-Baxter equation related to U_q (gl(2)) algebra and associated integrable lattice models
• Quantum elliptic algebras and double Yangians
• Braided doubles