Non-restricted representations of simple Lie superalgebras of special type and Hamiltonian type
type: Item
instance of: scholarly article
title: Non-restricted representations of simple Lie superalgebras of special type and Hamiltonian type
zbMATH Open document ID: 1275.17034
published in: Science China. Mathematics
publication date: 2013-04-08T00:00:00Z
review text: Let \(\mathbb{F}\) be an algebraically closed field of prime characteristic \(p > 2\), and \(\mathfrak g\) be a simple Lie superalgebra of special type or Hamiltonian type over \(\mathbb{F}\). The author first constructs the simple \(\mathfrak g\)-modules with non-singular characters, and prove the simplicity of the \(\chi\)-reduced Kac modules, where \(\chi\) is a non-singular character of height more than one. The author then constructs some simple modules with singular characters, and proves the simplicity of the \(\chi\)-reduced Kac modules, where \(\chi\) is a singular character of so-called \(\delta\)-invertible type. Furthermore, for the case of special type Lie superalgebras, the author also studies a class of reduced Kac modules with regular semisimple characters of height one, and it is to be simple.
reviewed by: Liangyun Chen
Mathematics Subject Classification ID: 17B50
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 17B35
zbMATH DE Number: 6151457
zbMATH Keywords: restricted Lie superalgebra
zbMATH Keywords: special Lie superalgebra
zbMATH Keywords: Hamiltonian Lie superalgebra
zbMATH Keywords: non-restricted representation
zbMATH Keywords: singular (non-singular) character
author: Yu-Feng Yao
MaRDI profile type: Publication
full work available at URL: s11425-012-4486-8
OpenAlex ID: W2128908205
cites work: Modular Representation Theory of Lie Algebras
cites work: Lie superalgebras
cites work: Automorphism Groups of Restricted Cartan-Type Lie Superalgebras
cites work: Identities in the enveloping algebras for modular Lie superalgebras
cites work: Character formulas for restricted simple modules of the special superalgebras
cites work: Restricted representations of the Witt superalgebras
cites work: Representations of the restricted Cartan type Lie superalgebra \(W(m,n,1)\)
cites work: Representations of the Witt algebra
cites work: Q4039778
cites work: Representations of Lie superalgebras in prime characteristic I
cites work: Representations of Lie superalgebras in prime characteristic. II: The queer series
cites work: Representations of the restricted Lie algebras of Cartan type
cites work: On the simple modules for the restricted Lie superalgebra \(\text{sl}(n|1)\)
cites work: Representations of Lie superalgebras in prime characteristic. III.
DOI: 10.1007/S11425-012-4486-8
description: scientific article; zbMATH DE number 6151457