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arXiv · 2305.18604

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

N. I. Stoilova·J. Van der Jeugt
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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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BibTeXRIS

N. I. Stoilova, J. Van der Jeugt. 2023-05-29. On classical $Z_2 \times Z_2$-graded Lie algebras. https://doi.org/10.1063/5.0149175

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