THE SECOND COHOMOLOGY GROUP OF ELEMENTARY QUADRATIC LIE SUPERALGEBRAS
Keywords:
cohomology, quadratic Lie superalgebras, super-exterior algebra, double extension, adjoint orbits
Abstract
By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we give a new way of description of the cohomology group of quadratic Lie superalgebras by applying the super-Poisson bracket on the super exterior algebra. Moreover, we calculate all of the second cohomology group of elementary quadratic Lie superalgebras which have been classified in [5].
Published
2021-07-20
Section
Articles