论文标题
拉格朗日和正交分裂，准二元谎言lie bialgebras和几乎复杂的产物结构
Lagrangian and orthogonal splittings, quasitriangular Lie bialgebras and almost complex product structures
论文作者
论文摘要
我们研究了二次向量空间的拉格朗日和正交分组\ textbf {\}，以建立具有复杂产品结构的等价。然后，我们表明，一个配备了通用度量$ \ Mathcal {g}+％\ Mathcal {B} $的Manin三重，以至于$ \ Mathcal {B} $是$ \ Mathcal {o} $ - 带有stectension $ \ nathcal {g} $ -1的运算符，也可以在另一个manin spplit中，或者在另一个manin split中旋转。在\ textbf {\}中说谎。相反，一对抗异态谎言代数的二次谎言代数直接总和与上一个案例相似的步骤后，可以用一个曼宁三重，承认正交分裂成谎言理想。
We study Lagrangian and orthogonal splittings\textbf{\ }of quadratic vector spaces establishing an equivalence with complex product structures. Then we show that a Manin triple equipped with generalized metric $\mathcal{G}+% \mathcal{B}$ such that $\mathcal{B}$ is an $\mathcal{O}$-operator with extension $\mathcal{G}$ of mass -1 can be turned in another Manin triple that admits also an orthogonal splitting in\textbf{\ }Lie ideals. Conversely, a quadratic Lie algebra orthogonal direct sum of a pair anti-isomorphic Lie algebras, after similar steps as in the previous case, can be turned in a Manin triple admitting an orthogonal splitting into Lie ideals.
