Cayley-Klein contractions of orthosymplectic superalgebras

TL;DR

This paper introduces a new class of orthosymplectic superalgebras derived from classical ones through contractions and analytic continuations, expanding the algebraic framework for superalgebra analysis.

Contribution

It defines the orthosymplectic superalgebras $osp(m;j|2n;\omega)$ and demonstrates their derivation from $osp(m|2n)$ via contractions and continuations, with specific examples.

Findings

Defined new superalgebra class $osp(m;j|2n;\omega)$

Showed how to obtain these from classical superalgebras

Provided examples with $osp(1|2)$ and $osp(3|2)$

Abstract

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