Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1895019 | Journal of Geometry and Physics | 2010 | 21 Pages |
Abstract
An odd-quadratic Lie superalgebra is a Lie superalgebra with a non-degenerate, supersymmetric, odd, and invariant bilinear form. In this paper we give examples and present some properties of odd-quadratic Lie superalgebras. We introduce the notions of double extension and generalized double extension of odd-quadratic Lie superalgebras and give an inductive description of solvable odd-quadratic Lie superalgebras and of odd-quadratic Lie superalgebras such that the even part is a reductive Lie algebra. We obtain also another interesting description of odd-quadratic Lie superalgebras such that the even part is a reductive Lie algebra without using the notions of double extensions.
Keywords
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Helena Albuquerque, Elisabete Barreiro, Saïd Benayadi,