Extensions, crossed modules and pseudoquadratic Lie type superalgebras

• M. Pouye ^[1] ; B. Kpamegan ^[2]
  1. [1] Institut de Mathématiques et de Sciences Physiques (IMSP), Bénin
  2. [2] Département de Mathématiques, FAST, UAC, Bénin
• Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 37, Nº 2, 2022, págs. 153-184
• Idioma: inglés
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• Resumen

  • 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