# Split Casimir operator and solutions of the Yang–Baxter equation for the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras, higher Casimir operators, and the Vogel parameters

@article{Isaev2022SplitCO,
title={Split Casimir operator and solutions of the Yang–Baxter equation for the

\$\$osp(M|N)\$\$
and

\$\$s\ell(M|N)\$\$
Lie superalgebras, higher Casimir operators, and the Vogel parameters},
author={A. P. Isaev and A. A. Provorov},
journal={Theoretical and Mathematical Physics},
year={2022},
volume={210},
pages={224-260}
}
• Published 16 January 2022
• Mathematics
• Theoretical and Mathematical Physics
Abstract We find the characteristic identities for the split Casimir operator in the defining and adjoint representations of the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras. These identities are used to build the projectors onto invariant subspaces of the representation $$T^{\otimes 2}$$ of the $$osp(M|N)$$ and $$s\ell(M|N)$$ Lie superalgebras in the cases where $$T$$ is the defining or adjoint representation. For the defining representation, the $$osp(M|N)$$ - and s\ell(M|N…

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