Fine group gradings of the real forms of $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$

Details Fine group gradings of the real forms of $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$ Fine group gradings of the real forms of $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$

2006-08-14

arxiv.org/abs/math-ph/0608032v2

Physics

Mathematical Physics

19 pages

Scientific paper

10.1063/1.2778543

We present an explicit description of the 'fine group gradings' (i.e. group gradings which cannot be further refined) of the real forms of the semisimple Lie algebras $sl(4,\C)$, $sp(4,\C)$, and $o(4,\C)$. All together 12 real Lie algebras are considered, and the total of 44 of their fine group gradings are listed. The inclusions $sl(4,\C)\supset sp(4,\C)\supset o(4,\C)$ are an important tool in our presentation. Systematic use is made of the faithful representations of the three Lie algebras by $4\times 4$ matrices.

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