On contractions of classical basic superalgebras

TL;DR

This paper introduces a class of superalgebras derived from classical superalgebras through contractions and analytic continuations, extending the Cayley-Klein framework to superalgebra structures.

Contribution

It defines new orthosymplectic and unitary superalgebras via contractions and continuations, and derives their Casimir operators from classical counterparts.

Findings

Construction of superalgebras via contractions and continuations.

Derivation of Casimir operators for Cayley-Klein superalgebras.

Examples include contractions of sl(2|1) and osp(3|2).

Abstract

We define a class of orthosymplectic $osp(m;j|2n;\omega)$ and unitary $sl(m;j|n;\epsilon)$ superalgebras which may be obtained from $osp(m|2n)$ and $sl(m|n)$ by contractions and analytic continuations in a similar way as the special linear, orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Casimir operators of Cayley-Klein superalgebras are obtained from the corresponding operators of the basic superalgebras. Contractions of $sl(2|1)$ and $osp(3|2)$ are regarded as an examples.