The Quantum Symmetry of Rational Field Theories
J\"urgen Fuchs
TL;DR
This paper explores the algebraic structures underlying the quantum symmetries in rational quantum field theories, focusing on their categorical properties and implications for classification.
Contribution
It provides a detailed analysis of the algebraic and categorical structures of quantum symmetries in rational field theories and discusses classification prospects.
Findings
Quantum symmetries form finite-dimensional multi-matrix algebras.
Representation categories are braided monoidal C*-categories.
Properties and classification ideas of these structures are outlined.
Abstract
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.)
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