Structure of Clifford-Weyl Algebras And Representations of ortho-symplectic Lie Superalgebras

TL;DR

This paper explores the structure and representations of Clifford-Weyl superalgebras and their associated ortho-symplectic Lie superalgebras, emphasizing their invariant inner products and physical applications.

Contribution

It provides a detailed analysis of the algebraic structure, tensor realizations, and representation theory of Clifford-Weyl superalgebras, including star structures for physical relevance.

Findings

Clifford-Weyl superalgebras can be realized as tensor products of alternating and symmetric tensors.

Invariant supersymmetric inner products are established on these superalgebras.

Representation descriptions of ortho-symplectic Lie superalgebras within these structures are provided.

Abstract

In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra structures. The Clifford-Weyl superalgebras can be realized as tensor product of the algebra of alternating and symmetric tensors respectively, on the even and odd parts of their underlying superspace. For Physical applications in elementary particles, we add star structures to these algebras and investigate the basic relations. Ortho-symplectic Lie algebras are naturally present in these algebras and their representations on these algebras can be described easily.