Super-de Sitter and alternative super-Poincaré symmetries

Abstract

It is well-known that de Sitter Lie algebra $\mathfrak{o}(1,4)$ contrary to anti-de Sitter one $\mathfrak{o}(2,3)$ does not have a standard ${\mathbb{Z}}_2$-graded superextension. We show here that the Lie algebra $\mathfrak{o}(1,4)$ has a superextension based on the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-grading. Using the standard contraction procedure for this superextension we obtain an {\it alternative} super-Poincaré algebra with the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-grading.

10 pages, X. International Workshop LIE THEORY AND ITS APPLICATIONS IN PHYSICS, (Varna, Bulgaria, 2013)

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