کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6414625 | 1630507 | 2014 | 41 صفحه PDF | دانلود رایگان |
In this paper, we generalize some results on quadratic Lie algebras to quadratic Lie superalgebras, by applying graded Lie algebras tools. We establish a one-to-one correspondence between non-Abelian quadratic Lie superalgebra structures and nonzero even super-antisymmetric 3-forms satisfying a structure equation. An invariant number of quadratic Lie superalgebras is then defined, called the dup-number. Singular quadratic Lie superalgebras (i.e. those with nonzero dup-number) are studied. We show that their classification follows the classifications of O(m)-adjoint orbits of o(m) and Sp(2n)-adjoint orbits of sp(2n). An explicit formula for the quadratic dimension of singular quadratic Lie superalgebras is also provided. Finally, we discuss a class of 2-nilpotent quadratic Lie superalgebras associated to a particular super-antisymmetric 3-form.
Journal: Journal of Algebra - Volume 407, 1 June 2014, Pages 372-412