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Braided Near-group Categories

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arxiv math/0011037 v1 pith:RDKLPYAV submitted 2000-11-06 math.QA math.AT

Jacob A. Siehler This is my paper · ORCID
classification math.QAmath.AT
keywords near-groupbraidedcategoriescategoryadditivelyassociativityclassifycommutativity
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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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  1. A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes

    quant-ph 2019-08 conditional novelty 6.0 of 10

    Self-inverse twists with invariant localisable charges in k stacked surface codes realize the kth level of a Tambara-Yamagami hierarchy whose braiding implements tensor products of S or CZ gates.

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