Exceptional quantum subgroups for the rank two Lie algebras B2 and G2

TL;DR

This paper classifies exceptional quantum subgroups for rank two Lie algebras B2 and G2 by analyzing conformal embeddings, quantum symmetries, and module structures, providing explicit algebraic and graph-based characterizations.

Contribution

It identifies and characterizes exceptional quantum subgroups for B2 and G2 Lie algebras, including their algebraic structures and associated graphs, expanding understanding of quantum symmetries.

Findings

Explicit algebraic structures of quantum symmetries determined.

Graphs describing exceptional quantum subgroups constructed and analyzed.

Global dimensions of the subgroups computed.

Abstract

Exceptional modular invariants for the Lie algebras B2 (at levels 2,3,7,12) and G2 (at levels 3,4) can be obtained from conformal embeddings. We determine the associated alge bras of quantum symmetries and discover or recover, as a by-product, the graphs describing exceptional quantum subgroups of type B2 or G2 which encode their module structure over the associated fusion category. Global dimensions are given.