Current algebras and categorified quantum groups

Current algebras and categorified quantum groups

We identify the trace, or zeroth Hochschild homology, of categorified quantum groups of ADE type 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 Khovanov‐L...

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Bibliographic Details
Published in:Journal of the London Mathematical Society Vol. 95; no. 1; pp. 248 - 276
Main Authors: Beliakova, Anna, Habiro, Kazuo, Lauda, Aaron D., Webster, Ben
Format: Journal Article
Language:English
Published: 01-02-2017
Subjects:
17B65
17B67
18D05
18D99 (primary)
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Summary:We identify the trace, or zeroth Hochschild homology, of categorified quantum groups of ADE type 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 Khovanov‐Lauda‐Rouquier algebras correspond to local (or global) Weyl modules. We also investigate the implications for centers of categories in 2‐representations of categorified quantum groups.
Bibliography:Anna Beliakova was supported by Swiss National Science Foundation under grant PDFMP2‐141752/1. Kazuo Habiro was supported by JSPS grant‐in‐aid for scientific research (C) 24540077. Aaron D. Lauda was partially supported by NSF grant DMS‐1255334 and the John Templeton Foundation. Ben Webster was supported by the NSF under grant DMS‐1151473.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms.12001