Coreductivity and cosymmetry of a Lie bialgebra are defined and shown to characterize when the complementary dual homogeneous space is reductive or symmetric, with applications to κ-deformed Lorentzian spacetimes.
Quantization of Poisson algebraic groups and Poisson homogeneous spaces
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abstract
This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the second part we apply our techniques of quantization to obtain some nontrivial examples of quantization of Poisson homogeneous spaces.
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Coisotropic Lie bialgebras and complementary dual Poisson homogeneous spaces
Coreductivity and cosymmetry of a Lie bialgebra are defined and shown to characterize when the complementary dual homogeneous space is reductive or symmetric, with applications to κ-deformed Lorentzian spacetimes.