Description: |
Lie bi-superalgebras arise in the theory of quantum mechanical integrable models and are related to the graded classical Yang-Baxter equation. By a triangular Lie bi-superalgebra we mean a Lie bi-superalgebra which co-multiplication comes from an even skew-symmetric solution of the classical Yang-Baxter equation. A Lie superalgebra is quadratic symplectic if it is equipped with both an invariant scalar product and a symplectic structure. In this talk we emphasize the correspondence between Lie bi-superalgebras and Manin superalgebras, via the double of a Lie bi-superalgebra. We also study triangular Lie bi-superalgebras, quadratic symplectic Lie superalgebras and investigate the connection between them. We show that a quadratic Lie superalgebra such that is also a triangular Lie bi-superalgebra is provided with a symplectic structure. We present an inductive description of quadratic symplectic Lie superalgebras. This is a joint work with Said Benayadi.
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