Quantum Dimensions and Quantum Galois Theory
Chongying Dong, Xiangyu Jiao, Feng Xu
TL;DR
This paper explores quantum dimensions in vertex operator algebras, establishing their properties, possible values, and a Galois theory framework for rational cases, advancing understanding of algebraic symmetries.
Contribution
It introduces a comprehensive Galois theory for rational vertex operator algebras based on quantum dimensions, including criteria for simple currents.
Findings
Quantum dimensions are characterized and their possible values are determined.
A criterion for identifying simple currents is provided.
A full Galois theory for rational vertex operator algebras is established.
Abstract
The quantum dimensions of modules for vertex operator algebras are defined and their properties are discussed. The possible values of the quantum dimensions are obtained for rational vertex operator algebras. A criterion for simple currents of a rational vertex operator algebra is given. A full Galois theory for rational vertex operator algebras is established using the quantum dimensions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra