Thursday, July 25, 2013

1307.6485 (Prince K Osei et al.)

Classical r-matrices via semidualisation    [PDF]

Prince K Osei, Bernd J Schroers
We study the interplay between double cross sum decompositions of a given Lie algebra and classical r-matrices for its semidual. For a class of Lie algebras which can be obtained by a process of generalised complexification we derive an expression for classical r-matrices of the semidual Lie bialgebra in terms of the data which determines the decomposition of the original Lie algebra. Applied to the local isometry Lie algebras arising in three-dimensional gravity, decomposition and semidualisation yields a complete list of non-trivial r-matrices for the Euclidean and Poincare group in three dimensions. In addition, the construction links the r-matrices with the Bianchi classification of three dimensional real Lie algebras.
View original:

No comments:

Post a Comment