A Jordan-H\" older theorem for weakly group-theoretical fusion categories
Sonia Natale
TL;DR
This paper extends the Jordan-Hölder theorem to weakly group-theoretical fusion categories, enabling the definition of composition factors and length as Morita invariants, thus advancing the structural understanding of these categories.
Contribution
It introduces a Jordan-Hölder theorem for weakly group-theoretical fusion categories and defines their composition factors and length as Morita invariants.
Findings
Established a Jordan-Hölder theorem for weakly group-theoretical fusion categories
Defined composition factors and length as Morita invariants
Provided a framework for analyzing the structure of such categories
Abstract
We prove a version of the Jordan-H\" older theorem in the context of weakly group-theoretical fusion categories. This allows us to introduce the composition factors and the length of such a fusion category C, which are in fact Morita invariants of C.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra