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Strict quantum 2-groups

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arxiv 1208.6265 v1 pith:6FPJFTIH submitted 2012-08-30 math.QA math.CT

Shahn Majid This is my paper · ORCID
classification math.QAmath.CT
keywords crossedgroupoidquantumbraidedgroupgroupsmodulenotion
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A crossed module is (A,H,d,\la) where d:A\to H is a homomorphism of groups and H acts on A, with conditions leading to a groupoid A\lcross H{\to\atop \to}H as an example of a strict 2-group. We give the corresponding notion of a quantum 2-group where we replace the above by Hopf algebras and introduce a new version of quantum groupoid. The work also suggests a natural notion of braided crossed module where A a braided-Hopf algebra in the braided category Z({}_H\CM) of crossed H-modules, although without the full groupoid picture in this more general case.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Categorical quantum symmetries and ribbon tensor 2-categories

    math-ph 2025-01 reject novelty 5.0 of 10

    The paper constructs ribbon balancing data and framing levels for 2Rep(U_q G), making it a candidate ribbon tensor 2-category, and recovers strict pivotality in the classical limit q=1.

  2. On coherent Hopf 2-algebras

    math.QA 2020-05 unverdicted novelty 4.0 of 10

    Constructs coherent Hopf 2-algebras via Hopf coquasigroups relaxing coassociativity, generalizing prior results, with examples from quasi-coassociative cases and Cayley algebra function algebras.

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