Quantum double finite group algebras and their representations

1993/10/01 by M.D. Gould, M. D. Gould · 46 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Braid group #Group (periodic table) #Irreducible representation #Mathematics #Pure mathematics #Quantum group #Quantum mechanics #Simple (philosophy) #Unitary group #Unitary state

paper · pdf · doi:10.1017/s0004972700015707

published in Bulletin of the Australian Mathematical Society 48(2), 275-301 (Cambridge University Press)

openalex publication_date 1993/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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

• On the Drinfeld double of a finite group scheme and its representation category
• Stacking and the triviality of invertible phases
• Simple Yetter-Drinfeld modules over infinite-dimensional Taft algebras
• Partition function of the Kitaev quantum double model
• Composite-Dimensional Topological Codes with Boundaries and Defects
• Finite dimensional Nichols algebras over Suzuki algebra II: over simple Yetter-Drinfeld modules of A_{N 2n+1}^μλ
• On the Structure of Irreducible Yetter-Drinfeld Modules over Quasi-Triangular Hopf Algebras
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• From entanglement renormalisation to the disentanglement of quantum double models
• 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