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Jianrong Li
Jianrong Li
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What is the current status of the classifications of Lie bialgebras? In particular, has the following problem been solved? Let $gl_n$ be the general linear Lie algebra. Classify all Lie cobrackets $\delta: gl_n \to \Lambda^2 gl_n$. Any help will be greatly appreciated!

Edit: it seems that the case that $g$ is a semisimple Lie algebra is done by Belavin and Drinfeld.

What is the current status of the classifications of Lie bialgebras? In particular, has the following problem been solved? Let $gl_n$ be the general linear Lie algebra. Classify all Lie cobrackets $\delta: gl_n \to \Lambda^2 gl_n$. Any help will be greatly appreciated!

What is the current status of the classifications of Lie bialgebras? In particular, has the following problem been solved? Let $gl_n$ be the general linear Lie algebra. Classify all Lie cobrackets $\delta: gl_n \to \Lambda^2 gl_n$. Any help will be greatly appreciated!

Edit: it seems that the case that $g$ is a semisimple Lie algebra is done by Belavin and Drinfeld.

Source Link
Jianrong Li
Jianrong Li
  • 6.2k
  • 2
  • 21
  • 34

Classifications of Lie bialgebras

What is the current status of the classifications of Lie bialgebras? In particular, has the following problem been solved? Let $gl_n$ be the general linear Lie algebra. Classify all Lie cobrackets $\delta: gl_n \to \Lambda^2 gl_n$. Any help will be greatly appreciated!