The quantum spin Brauer category

2025/04/23 by Peter J. McNamara, McNamara, Peter J., Alistair Savage +1 · 1 citation
Materials Science · Mathematics · #17B37 #18M15 #18M30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Magnetism in coordination complexes #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2504.16618

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

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 1 modules for U_q(\mathfrakso(N)) or U_q(\mathfrako(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.

Citations

• Webs for the Quantum Orthogonal Group
• A basis theorem for the affine Kauffmann category and its cyclotomic quotients
• Dualities for spin representations
• Webs and q-Howe dualities in types \mathbf BCD
• Webs and quantum skew Howe duality
• The Brauer Category and Invariant Theory
• Symmetrizers and antisymmetrizers for the BMW algebra
• On centralizer algebras for spin representations
• A survey of graphical languages for monoidal categories
• On braided tensor categories of type BCD
• Symmetrizer and Antisymmetrizer of the Birman-Wenzl-Murakami Algebras
• Introduction to quantum groups
• Quantum symmetric spaces and related q-orthogonal polynomials
• q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations
• Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

Cited by

• The disoriented skein and iquantum Brauer categories

Related

• A category of quantum categories
• The disoriented skein and iquantum Brauer categories
• Quantum Webs of Type Q
• Modular categories of types B,C and D
• Quantum modules