Extensions, crossed modules and pseudo quadratic Lie type superalgebras - POUYE, Mamadou; KPAMEGAN, ASSOGBA BERNARDIN (My University, 2022)
Extensions and crossed modules of Lie type superalgebras are introduced and studied. We construct homology and cohomology theories of Lie-type superalgebras. The notion of left super-invariance for a bilinear form is defined and we consider Lie type superalgebras endowed with nondegenerate, supersymmetric and left super-invariant bilinear form. Such Lie type superalgebras are called pseudo quadratic Lie type superalgebras. We show that any pseudo quadratic Lie type superalgebra induces a Jacobi-Jordan superalgebra. By using the method of double extension, we study pseudo quadratic Lie type superalgebras and theirs associated Jacobi-Jordan superalgebras.
Keywords: Lie type superalgebras; Jacobi-Jordan superalgebras; extension; crossed module; homology; cohomology; double extension; pseudo quadratic Lie type superalgebras.