It is proved that there exist no simple finite-dimensional Filippov superalgebras of type A(n, n) over an algebraically closed field of characteristic 0.
Abstract. A study of real skew-symmetric matrices of orders 7 and 8, defined through the vector cross product in R 7 , is presented. More concretely, results on matrix properties, eigenvalues, (generalized) inverses and rotation matrices are established.
The algebraic and geometric classification of all complex 3-dimensional transposed Poisson algebras is obtained. Also we discuss special 3-dimensional transposed Poisson algebras.
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