On a class of Fock-like representations for Lie Superalgebras

Abstract

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.

33 pages, Work initiated during postdoctoral stay of the first author, at IFM, UMSNH, Morelia, Michoacan, Mexico (in progress). v2 contains new material and constitutes a significantly expanded version of the text

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Cited by in corpus (2)

• Gradings, Braidings, Representations, Paraparticles: some open problems
• Towards applications of graded Paraparticle algebras