Quantization of inhomogeneous Lie bialgebras

✍ Scribed by P.P. Kulish; A.I. Mudrov

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 120 KB
• Volume: 42
• Category: Article
• ISSN: 0393-0440
• DOI: 10.1016/s0393-0440(01)00073-0

✦ Synopsis

A self-dual class of Lie bialgebra structures (g, g * ) on inhomogeneous Lie algebras g describing kinematical symmetries is considered. In that class, both g and g * split into the semi-direct sums g = h v and g * = h * v * with abelian ideals of translations v and h * . We build the explicit quantization of the universal enveloping algebra U(g), including the coproduct, commutation relations among generators, and, in case of coboundary g, the universal R-matrix. This class of Lie bialgebras forms a self-dual category stable under the classical double procedure. The quantization turns out to be a functor to the category of Hopf algebras which commutes with operations of dualization and double.