Some remarks on relative modular categories
Nathan Geer, Bertrand Patureau-Mirand, Matthew Rupert
TL;DR
This paper investigates the properties of relative modular categories, establishing conditions for their non-degeneracy, modularity, and semi-simplicity of certain quotients, advancing the theoretical understanding of these algebraic structures.
Contribution
It provides new sufficient conditions for the existence and properties of relative modular categories, including criteria for non-degeneracy and semi-simplicity.
Findings
Derived conditions for relative pre-modular categories to be non-degenerate
Established criteria for relative modularity
Showed when quotients by negligible modules are semi-simple
Abstract
We study properties of relative modular categories and derive sufficient conditions for their existence. In particular, we derive sufficient conditions for relative pre-modular categories to be non-degenerate and relative modular, and for the quotient of categories taking a particular form by their ideal of negligible modules to be generically semi-simple.
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Taxonomy
TopicsVascular Malformations Diagnosis and Treatment · Rings, Modules, and Algebras · Intracranial Aneurysms: Treatment and Complications