English

The quantum spin Brauer category

Quantum Algebra 2025-04-24 v1 Representation Theory

Abstract

We introduce a diagrammatic braided monoidal category, the quantum spin Brauer category, together with a full functor to the category of finite-dimensional, type 11 modules for Uq(so(N))U_q(\mathfrak{so}(N)) or Uq(o(N))U_q(\mathfrak{o}(N)). This functor becomes essentially surjective after passing to the idempotent completion. The quantum spin Brauer category can be thought of as a quantum version of the spin Brauer category introduced previously by the authors. Alternatively, it is an enlargement of the Kauffman category, obtained by adding a generating object corresponding to the quantum spin module.

Keywords

Cite

@article{arxiv.2504.16618,
  title  = {The quantum spin Brauer category},
  author = {Peter J. McNamara and Alistair Savage},
  journal= {arXiv preprint arXiv:2504.16618},
  year   = {2025}
}

Comments

44 pages

R2 v1 2026-06-28T23:08:25.476Z