Subalgebras of etale algebras and fusion subcategories

2021/05/24 by Burciu, Sebastian
#Category Theory (math.CT) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2105.11202

Abstract

In \cite[Rem. 3.4]DNO the authors asked the question if any étale subalgebra of an étale algebra in a braided fusion category is also étale. We give a positive answer to this question if the braided fusion category \cc is pseudo-unitary and non-degenerate. In the case of a pseudo-unitary fusion category we also give a new description of the lattice correspondence from \cite[Theorem 4.10]DMNO. This new description enables us to describe the two binary operations on the lattice of fusion subcategories.

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