On classical $Z_2 \times Z_2$-graded Lie algebras
Mathematical Physics
2023-09-12 v2 Group Theory
math.MP
Rings and Algebras
Representation Theory
Abstract
We construct classes of -graded Lie algebras corresponding to the classical Lie algebras, in terms of their defining matrices. For the -graded Lie algebra of type , the construction coincides with the previously known class. For the -graded Lie algebra of type , and 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.
Keywords
Cite
@article{arxiv.2305.18604,
title = {On classical $Z_2 \times Z_2$-graded Lie algebras},
author = {N. I. Stoilova and J. Van der Jeugt},
journal= {arXiv preprint arXiv:2305.18604},
year = {2023}
}