Nil-Brauer categorifies the split iquantum group of rank one Article Swipe

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Mathematics Brauer group Indecomposable module Pure mathematics Basis (linear algebra) Isomorphism (crystallography) Rank (graph theory) Quantum Group (periodic table) Projective module Tensor product Projective test Algebra over a field Discrete mathematics Combinatorics Geometry Crystallography Chemistry Physics Crystal structure Organic chemistry Quantum mechanics

Jonathan Brundan , Weiqiang Wang , Ben Webster ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2305.05877 · OA: W4376166997

We prove that the Grothendieck ring of the monoidal category of finitely generated graded projective modules for the nil-Brauer category is isomorphic to an integral form of the split iquantum group of rank one. Under this isomorphism, the indecomposable graded projective modules correspond to the icanonical basis. We also derive character formulae for irreducible graded modules and deduce various branching rules.