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.

References in corpus (4)

• Once more on parastatistics
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded Lie Symmetries of the Lévy-Leblond Equations
• The parafermion Fock space and explicit so(2n+1) representations
• Is the ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded sine-Gordon equation integrable?

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