δ-BiHom-Jordan-李超代数的阿贝尔扩张和T^(*)-扩张

Abelian extensition andT^(*)-extensions ofδ-Bi Hom-Jordan Lie superalgebras

引入了δ-BiHom-Jordan-李超代数的阿贝尔扩张,并证明其与任意阿贝尔扩张相关联的一个表示和一个2-余循环。此外,验证了特征不为2的代数闭域上的有限维幂零二次δ-BiHom-Jordan-李超代数与δ-幂零BiHom-Jordan李超代数T^(*)-扩张等距。

This paper introduces Abelian extensions ofδ-BiHom-Jordan Lie superalgebras and show that there is a representation and a 2-cocycle,associated to any Abelian extension.Moreover,we prove that every finite-dimensional nilpotent quadraticδ-BiHom-Jordan Lie superalgebra over an algebraically closed field of characteristic not 2 is isometric to a T^(*)-extension of a nilpotentδ-BiHom-Jordan Lie superalgebra.