摘要
Let L be a contragredient Lie superalgebra. A symmetric pair of L is a pair (g, g σ ) , where g is a real form of L, and σ is a g-involution with invariant subalgebra g σ . We show that a symmetric pair carries invariant symplectic forms if and only if g σ has a 1-dimensional center. Furthermore, the symplectic form is pseudo-Kähler if and only if the center of g σ is compact. As an application, we classify the symplectic symmetric pairs, as well as the pseudo-Kähler symmetric pairs.