Lie bialgebras of generalized Witt type

Details Lie bialgebras of generalized Witt type Lie bialgebras of generalized Witt type

2005-04-08

arxiv.org/abs/math/0504168v1

Mathematics

Quantum Algebra

14 pages

Scientific paper

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.

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