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arXiv · 2007.01642

Foundations of Frobenius Heisenberg categories

Jonathan Brundan·Alistair Savage·Ben Webster
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Abstract

We describe bases for the morphism spaces of the Frobenius Heisenberg categories associated to a symmetric graded Frobenius algebra, proving several open conjectures. Our proof uses a categorical comultiplication and generalized cyclotomic quotients of the category. We use our basis theorem to prove that the Grothendieck ring of the Karoubi envelope of the Frobenius Heisenberg category recovers the lattice Heisenberg algebra associated to the Frobenius algebra.

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Jonathan Brundan, Alistair Savage, Ben Webster. 2023-09-27. Foundations of Frobenius Heisenberg categories. https://doi.org/10.1016/j.jalgebra.2021.02.025

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