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This is a Quantitative Study study.

October 13, 2025Open Access

Categorification of quantum boson algebras

Key Points

The construction produces interesting bases for quantum boson algebras and quantum bosonic extensions.
Our categorifications are defined through diagrammatic generators and relations, enhancing structure understanding.
The 2-representation on Khovanov-Lauda and Rouquier's positive part quantum group confirms the effectiveness of our approach.
Findings offer a new framework for examining quantum boson algebras in the realm of Kac-Moody types.

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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Cite This Study

Sam Qunell (Mon,) studied this question.

synapsesocial.com/papers/68ed1896f29694dd1da78b55 https://doi.org/https://doi.org/10.48550/arxiv.2509.12163

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