To join the seminar, connect to the Zoom meeting a few minutes prior to the beginning at (or manually by entering the meeting ID 812 2079 3393 in the Zoom app).By definition an algebra $B$ is binary-Lie algebra iff any two elements $a,b\in B$ generate a Lie subalgebra. A ${\bf Z}_2-$graded algebra $B=B_0\oplus B_1$ is a binary-Lie superalgebra iff $B\times \Gamma=B_0\otimes \Gamma_0\oplus B_1\otimes \Gamma_1$ is a binary Lie algebra, where $Gamma=Gamma_0\oplus Gamma_1$ is a Grassman algebra with natural gradation. We apply the theory of binary-Lie algebras for proving the following result.
Theorem. Let $B=B_0\oplus B_1$ be a simple binary-Lie superalgebra finite dimensional over the field ${\bf C}$ of complex numbers. Then $B_0$ is a solvable algebra or $B$ is a Lie superalgebra.
This theorem reduced the problem (open yet!) of classification of a simple binary-Lie superalgebra finite dimensional over the field ${\bf C}$ to the case where subalgebra $B_0$ is solvable.
This talk is based on the joint paper with A.Grishkov and I.Shestakov.
