2017/09/25 by Cao Tran Tu Hai, Hai, Cao Tran Tu, Duong Minh Thanh +3
Mathematics · #17B60 #FOS: Mathematics #Primary 17B #Rings and Algebras (math.RA) #Secondary 17B56 #math.RA #msc:17B #msc:17B56 #msc:17B60
paper · pdf · doi:10.48550/arxiv.1709.08582
15 pages
arxiv created 2017/09/25 · arxiv updated 2017/09/26
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 calculate all of the second cohomology group of elementary quadratic Lie superalgebras which have been classified in \citeDU14 by applying the super-Poisson bracket on the super exterior algebra. Besides, we give the classification of 8-dimensional solvable quadratic Lie superalgebras having 6-dimensional indecomposable even part. The method is based on the double extension and classification results of adjoint orbits of the Lie algebra \mathfraks\mathfrakp(2).