Smooth modules of the super \(\mathcal{W}\)-algebra \(\mathcal{SW}(\frac{3}{2}, \frac{3}{2})\) of Neveu-Schwarz type
type: Item
instance of: scholarly article
title: Smooth modules of the super \(\mathcal{W}\)-algebra \(\mathcal{SW}(\frac{3}{2}, \frac{3}{2})\) of Neveu-Schwarz type
author: Jinlu Li
author: Jiancai Sun
published in: Journal of Algebra
publication date: 2024-11-04T00:00:00Z
review text: The super \(W\)-algebra \(SW(\frac{3}{2},\frac{3}{2})\) (see [\textit{J. M. Figueroa-O'Farrill} and \textit{S. Schrans}, Int. J. Mod. Phys. A 7, No. 3, 591--617 (1992; Zbl 0801.17032)]) is a supersymmetric conformal algebra that incorporates an additional covariant supersymmetric field \(\Phi\) of dimension \((\frac{3}{2},2)\).\N\NIn the paper underestablish a connection between simple smooth modules over \(L\) and simple modules over specific finite-dimensional solvable Lie superalgebras. This relation is used to study smooth modules over the considered super \(W\)-algebras. In particular several examples including simple Whittaker modules and highest weight modules are given.
reviewed by: Dmitry Artamonov
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B66
Mathematics Subject Classification ID: 17B68
zbMATH DE Number: 7938149
zbMATH Keywords: \(\mathcal{SW}(\frac{3}{2}, \frac{3}{2})\) algebra
zbMATH Keywords: smooth module
zbMATH Keywords: simple module
MaRDI profile type: Publication
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DOI: 10.1016/J.JALGEBRA.2024.06.042
description: scientific article; zbMATH DE number 7938149