Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras

Details Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras

2005-03-25

arxiv.org/abs/math/0503608v1

Mathematics

Quantum Algebra

Scientific paper

We solve a functional version of the problem of twist quantization of a coboundary Lie bialgebra (g,r,Z). We derive from this the following results: (a) the formal Poisson manifolds g^* and G^* are isomorphic; (b) we construct a subalgebra of U(g^*), isomorphic to S(g^*)^g. When g can be quantized, we construct a deformation of the morphism S(g^*)^g subset U(g^*). When g is quasitriangular and nondegenerate, we compare our construction with Semenov-Tian-Shansky's construction of a commutative subalgebra of U(g^*). We also show that the canonical derivation of the function ring of G^* is Hamiltonian.

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