Braided Near-group Categories
Jacob A. Siehler
TL;DR
This paper classifies braided structures on near-group categories, providing explicit formulas for their associativity and commutativity morphisms, advancing understanding of their algebraic properties.
Contribution
It offers a complete classification of braided near-group categories and derives explicit formulas for their key morphisms, which was previously unknown.
Findings
Complete classification of braided near-group categories
Explicit formulas for associativity morphisms
Explicit formulas for commutativity morphisms
Abstract
A near-group category is an additively semisimple category with a product such that all but one of the simple objects is invertible. We classify braided structures on near-group categories, and give explicit numerical formulas for their associativity and commutativity morphisms.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra