Resumen de Extensions, crossed modules and pseudoquadratic Lie type superalgebras

M. Pouye, B. Kpamegan

• 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 leftsuper-invariance for a bilinear form is defined and we consider Lie type superalgebras endowed withnondegenerate, supersymmetric and left super-invariant bilinear form. Such Lie type superalgebrasare called pseudo quadratic Lie type superalgebras. We show that any pseudo quadratic Lie typesuperalgebra induces a Jacobi-Jordan superalgebra. By using the method of double extension, westudy pseudo quadratic Lie type superalgebras and theirs associated Jacobi-Jordan superalgebras