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arXiv · 1412.1417

Current algebras and categorified quantum groups

Anna Beliakova·Kazuo Habiro·Aaron D. Lauda·Ben Webster
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Abstract

We identify the trace, or 0th Hochschild homology, of type ADE categorified quantum groups with the corresponding current algebra of the same type. To prove this, we show that 2-representations defined using categories of modules over cyclotomic (or deformed cyclotomic) quotients of KLR-algebras correspond to local (or global) Weyl modules. We also investigate the implications for centers of categories in 2-representations of categorified quantum groups.

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Anna Beliakova, Kazuo Habiro, Aaron D. Lauda, Ben Webster. 2023-01-23. Current algebras and categorified quantum groups. https://doi.org/10.1112/jlms.12001

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