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- W2949326062 abstract "From a Lie algebra $mathfrak{g}$ satisfying $mathcal{Z}(mathfrak{g})=0$ and $Lambda^2(mathfrak{g})^mathfrak{g}=0$ (in particular, for $g$ semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form $mathfrak{L} =mathfrak{g}times mathbb{K}$ in terms of Lie bialgebra structures on $mathfrak{g}$ (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field $mathbb{K}$ with char $mathbb{K}=0$. If moreover, $[mathfrak{g},mathfrak{g}]=mathfrak{g}$, then we describe also all Lie bialgebra structures on extensions $mathfrak{L} =mathfrak{g}times mathbb{K}^n$. In interesting cases we characterize the Lie algebra of biderivations." @default.
- W2949326062 created "2019-06-27" @default.
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- W2949326062 date "2011-10-05" @default.
- W2949326062 modified "2023-09-27" @default.
- W2949326062 title "Trivial Central Extensions of Lie Bialgebras" @default.
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