Quantization of inhomogeneous Lie bialgebras

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 quant...

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Bibliographic Details
Published in:Journal of geometry and physics 2002-05, Vol.42 (1), p.64-77
Main Authors: Kulish, P.P., Mudrov, A.I.
Format: Article
Language:English
Subjects:
Inhomogeneous Lie bialgebras
Quantization
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(01)00073-0