1993/12/03 by Jürgen Fuchs, J�rgen Fuchs
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Braid group #Field (mathematics) #Fusion #Fusion rules #Geometry #Mathematics #Philosophy #Physics #Pure mathematics #Quantum #Quantum field theory #Quantum gravity #Quantum group #Quantum mechanics #Representation theory #Superselection #Symmetry (geometry) #Theoretical physics #hep-th
paper · pdf · doi:10.1007/bf01102203
published as Theor.Math.Phys. 98 (1994) 266-276; Teor.Mat.Fiz. 98 (1994) 388-403 · 16 pages (A4) in LaTeX
arxiv created 1993/12/03 · openalex publication_date 1994/03/01 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The quantum symmetry of a rational quantum field theory is a finite- dimensional multi-matrix algebra. Its representation category, which determines the fusion rules and braid group representations of superselection sectors, is a braided monoidal C^*-category. Various properties of such algebraic structures are described, and some ideas concerning the classification programme are outlined. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Teor.Mat.Fiz.)