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- Title
Extensions, crossed modules and pseudo quadratic Lie type superalgebras.
- Authors
POUYE, M.; KPAMEGAN, B.
- Abstract
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.
- Subjects
MODULES (Algebra); COHOMOLOGY theory; JACOBI varieties; MATHEMATICAL symmetry; BILINEAR forms
- Publication
Extracta Mathematicae, 2022, Vol 37, Issue 2, p153
- ISSN
0213-8743
- Publication type
Article
- DOI
10.17398/2605-5686.37.2.153