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Description: |
The notion of n-Lie superalgebra was introduced in 1996, by Daletskii and Kushnirevich, as a natural generalization of the n-Lie algebra concept due to Filippov (1985). Because of the actual tendency of Filippov's scientific followers, we will use the terms Filippov superalgebra and Filippov algebra, respectively, instead of the previous ones. We will present a summarized perspective of some aspects of the mentioned Lie algebras' relatives. Related to these, we will consider two problems: 1) the characterization of a triple system which is a ternary quaternion algebra with multiplication defined through the multiplication on the Filippov algebra A_1; 2) the classification of the finite-dimensional simple Filippov superalgebras over an algebraically closed field of characteristic zero.
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