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arXiv · 2509.12163

Categorification of quantum boson algebras

Sam Qunell
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Abstract

We produce graded monoidal categorifications of the quantum boson algebras in any symmetrizable Kac-Moody type. Our categories are defined in terms of diagrammatic generators and relations and have a faithful 2-representation on Khovanov-Lauda and Rouquier's categorification of the corresponding positive part quantum group. We use our construction to produce interesting bases of the quantum boson algebras and quantum bosonic extensions.

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Sam Qunell. 2025-09-15. Categorification of quantum boson algebras. https://arxiv.org/abs/2509.12163

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