Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

Chih Whi Chen; Kevin Coulembier; Volodymyr Mazorchuk

doi:10.1007/s00209-020-02510-y

Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

Chih Whi Chen, Kevin Coulembier, Volodymyr Mazorchuk

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that the tensor product of a simple and a finite dimensional sl_n-module has finite type socle. This is applied to reduce classification of simple q(n) -supermodules to that of simple sl_n-modules. Rough structure of simple q(n) -supermodules, considered as sl_n-modules, is described in terms of the combinatorics of category O.

Original language	English
Pages (from-to)	255-281
Number of pages	27
Journal	Mathematische Zeitschrift
Volume	297
Issue number	1-2
DOIs	https://doi.org/10.1007/s00209-020-02510-y
State	Published - Feb 2021

Keywords

Lie algebra
Lie superalgebra
Rough structure
Simple module
Simple supermodule
Socle
Tensor product

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abstract = "We prove that the tensor product of a simple and a finite dimensional sln-module has finite type socle. This is applied to reduce classification of simple q(n) -supermodules to that of simple sln-modules. Rough structure of simple q(n) -supermodules, considered as sln-modules, is described in terms of the combinatorics of category O.",

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AB - We prove that the tensor product of a simple and a finite dimensional sln-module has finite type socle. This is applied to reduce classification of simple q(n) -supermodules to that of simple sln-modules. Rough structure of simple q(n) -supermodules, considered as sln-modules, is described in terms of the combinatorics of category O.

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KW - Lie superalgebra

KW - Rough structure

KW - Simple module

KW - Simple supermodule

KW - Socle

KW - Tensor product

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Translated simple modules for Lie algebras and simple supermodules for Lie superalgebras

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Keywords

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