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Non-weight modules over N = 1 Lie superalgebras of Block type

  • Qiang Xie and Jiancai Sun EMAIL logo
Published/Copyright: June 1, 2023

Abstract

In this paper, a class of non-weight modules over N = 1 Lie superalgebras of Block type (without center) is studied. These modules over Ramond algebras of Block type are free of rank 1 when restricted to the universal enveloping algebra of the Cartan subalgebra, while such modules are free of rank 2 over the Neveu–Schwarz algebras of Block type. We present the classification of these modules. Furthermore, the simplicity of these modules is determined.

MSC 2020: 17B40; 17B65; 17B68

Communicated by Jan Frahm


Award Identifier / Grant number: 12071276

Award Identifier / Grant number: 11931009

Award Identifier / Grant number: 12226402

Funding statement: Jiancai Sun would like to thank the support of National Natural Science Foundation of China (Nos. 12071276, 11931009 and 12226402).

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Received: 2022-09-13
Revised: 2023-04-17
Published Online: 2023-06-01
Published in Print: 2023-09-01

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