Bounded Weight Modules Over the Lie Superalgebra of Cartan W-type

Let A m , n be the tensor product of the polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field ℂ , and the Witt superalgebra W m , n be the Lie superalgebra of superderivations of A m , n . In this paper, we classify the non-trivial simple bounded...

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Bibliographic Details
Published in:Algebras and representation theory 2023-06, Vol.26 (3), p.763-781
Main Authors: Lü, Rencai, Xue, Yaohui
Format: Article
Language:English
Subjects:
Associative Rings and Algebras
Commutative Rings and Algebras
Complex variables
Mathematical analysis
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
Polynomials
Tensors
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Summary:Let A m , n be the tensor product of the polynomial algebra in m even variables and the exterior algebra in n odd variables over the complex field ℂ , and the Witt superalgebra W m , n be the Lie superalgebra of superderivations of A m , n . In this paper, we classify the non-trivial simple bounded weight W m , n modules with respect to the standard Cartan subalgebra of W m , n . Any such module is a simple quotient of a tensor module F ( P , L ( V 1 ⊗ V 2 )) for a simple weight module P over the Weyl superalgebra K m , n , a finite-dimensional simple g l m -module V 1 and a simple bounded g l n -module V 2 .
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-021-10112-3