Classical r-matrices via semidualisation

Autor:	Osei, Prince K, Schroers, Bernd J
Rok vydání:	2013
Předmět:	Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory
Druh dokumentu:	Working Paper
DOI:	10.1063/1.4824704
Popis:	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 the main class 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. Comment: 21 pages, 1 figure, typos corrected
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1307.6485 Zobrazit plný text záznamu View this record from Arxiv