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Glasnik matematički, Vol. 57 No. 1, 2022.

Original scientific paper

https://doi.org/10.3336/gm.57.1.02

Finite W-algebras associated to truncated current Lie algebras

Xiao He ; Paris Curie Engineer School, Beijing University of Chemical Technology, P.R.China

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Abstract

Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \(s\ell_2\) case.

Keywords

Truncated current Lie algebras, Finite W-algebras, Skryabin equivalence, Whittaker modules.

Hrčak ID:

279797

URI

https://hrcak.srce.hr/279797

Publication date:

28.6.2022.

Visits: 888 *

Publication date: 30 June 2022

Volume: Vol 57

Issue: Svezak 1

Pages: 17-33

DOI: https://doi.org/10.3336/gm.57.1.02

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Truncated current Lie algebras, Finite W-algebras, Skryabin equivalence, Whittaker modules.

Finite W-algebras associated to truncated current Lie algebras

Xiao He[1]

Email: hexiao@amss.ac.cn

 

[1] Paris Curie Engineer School, Beijing University of Chemical Technology, P.R.China

Abstract

Finite W-algebras associated to truncated current Lie algebras are studied in this paper. We show that some properties of finite W-algebras in the semisimple case hold in the truncated current case. In particular, Kostant's theorem and Skryabin equivalence hold in our case. As an application, we give a classification of simple Whittaker modules for truncated current Lie algebras in the \(s\ell_2\) case.

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