On classical $Z_2\times Z_2$-graded Lie algebras

Abstract

We construct classes of $Z_2\times Z_2$-graded Lie algebras corresponding to the classical Lie algebras, in terms of their defining matrices. For the $Z_2\times Z_2$-graded Lie algebra of type $A$, the construction coincides with the previously known class. For the $Z_2\times Z_2$-graded Lie algebra of type $B$, $C$ and $D$ our construction is new and gives rise to interesting defining matrices closely related to the classical ones but undoubtedly different. We also give some examples and possible applications to parastatistics.

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Cited by in corpus (4)

• Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• Integrable ${\mathbb{Z}}_2^2$-graded Extensions of the Liouville and Sinh-Gordon Theories
• ${\mathbb{Z}}_2^2$-graded supersymmetry via superfield on minimal ${\mathbb{Z}}_2^2$-superspace
• Generalized Calogero-Moser system and supergroup gauge origami