Lagrangian and orthogonal splittings, quasitriangular Lie bialgebras and almost complex product structures
arXiv:2208.09996 · doi:10.1063/5.0127960
Abstract
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 such that is an -operator with extension 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.
26 pages. This is a corrected version. In the previous versions, the first proposition of section 2 contains an erroneous statement unrelated to the rest of the paper, so it has been removed from this new version and this section has been partially rewritten, with no other consequences