Abstract
The Casimir elements of the P-type Lie superalgebras are investigated. Depending on the class of algebras under consideration either there do not exist any nontrivial Casimir elements at all or else the Casimir elements are highly degenerate. Basic to the investigation is a lemma about invariant supersymmetric multilinear forms on a finite-dimensional module over a Lie superalgebra. Some comments on the Cartan subalgebras of a Lie superalgebra are also included. An Appendix provides some information on multilinear algebra with ε-commuting scalars.
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