IJPAM: Volume 40, No. 2 (2007)
THE POISSON SUBALGEBRAS OF COMPACT
SEMISIMPLE LIE BIALGEBRAS
SEMISIMPLE LIE BIALGEBRAS
Steven Benzel
Department of Mathematics
Berry College
Mount Berry, GA 30149-5036, USA
e-mail: sbenzel@berry.edu
Department of Mathematics
Berry College
Mount Berry, GA 30149-5036, USA
e-mail: sbenzel@berry.edu
Abstract.We begin by reviewing the definition of a Lie bialgebra and recall
some standard results.
The Lie bialgebra structures on a compact semisimple Lie bialgebra are then
determined using Soibelman's classification of such structures for a compact
simple Lie bialgebra. We then determine the
Poisson subalgebras for these structures. We conclude with some
straightforward remarks on the notion of Poisson homogeneous spaces.
Received: September 13, 2007
AMS Subject Classification: 17B62
Key Words and Phrases: Lie bialgebra, Poisson Lie group
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 2
