On a class of Fock-like representations for Lie Superalgebras

Utilizing Lie superalgebra (LS) realizations via the Relative Parabose Set algebra \(P_{BF}\), combined with earlier results on the Fock-like representations of \(P_{BF}^{(1,1)}\), we proceed to the construction of a family of Fock-like representations of LSs: these are infinite dimensional, decompo...

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Bibliographic Details
Published in:arXiv.org 2012-05
Main Authors: Kanakoglou, K, Herrera-Aguilar, A
Format: Article
Language:English
Subjects:
Decomposition
Lie groups
Representations
Online Access:Get full text
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Summary:Utilizing Lie superalgebra (LS) realizations via the Relative Parabose Set algebra \(P_{BF}\), combined with earlier results on the Fock-like representations of \(P_{BF}^{(1,1)}\), we proceed to the construction of a family of Fock-like representations of LSs: these are infinite dimensional, decomposable super-representations, which are parameterized by the value of a positive integer \(p\). They can be constructed for any LS \(L\), either initiating from a given 2-dimensional, \(\mathbb{Z}_{2}\)-graded representation of \(L\) or using its inclusion as a subalgebra of \(P_{BF}^{(1,1)}\). As an application we proceed in studying decompositions with respect to various low-dimensional Lie algebras and superalgebras.
ISSN:2331-8422