Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras

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

Carbon isotopes in bulk carbonaceous chondrites

The chemical and physical processes involved in the formation of the solar system are examined. Primitive matter has been found on a microscopic scale in a variety of meteorites: fragments of small solar system bodies that were never part of a large planet. This primitive matter has, in most cases, been identified by the presence of anomalous abundances of some isotopes of the chemical elements. Of particular interest for carbon isotope studies are the primitive meteorites known as carbonaceous chondrites. Using a selective oxidation technique to sort out the carbon contained in different chemical forms (graphite, carbonates, and organic matter), four carbonaceous chondrites are analyzed. The presence of the (13) C-rich component was confirmed and additional carbon components with different, but characteristic, isotopic signatures were resolved

Braiding structures on formal Poisson groups and classical solutions of the QYBE

If g is a quasitriangular Lie bialgebra, the formal Poisson group F[[g^*]] can be given a braiding structure. This was achieved by Weinstein and Xu using purely geometrical means, and independently by the authors by means of quantum groups. In this paper we compare these two approaches. First, we show that the braidings they produce share several similar properties (in particular, the construction is functorial); secondly, in the simplest case (G = SL_2) they do coincide. The question then rises of whether they are always the same this is positively answered in a separate paper

New rr-Matrices for Lie Bialgebra Structures over Polynomials

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to produce $r$-matrices which correspond to Lie bialgebra structures over polynomials

Uniqueness of braidings of quasitriangular Lie bialgebras and lifts of classical r-matrices

It is known that any quantization of a quasitriangular Lie bialgebra g gives rise to a braiding on the dual Poisson-Lie formal group G*. We show that this braiding always coincides with the Weinstein-Xu braiding. We show that this braiding is the “time one automorphism” of a Hamiltonian vector field, corresponding to a certain formal function on G* × G*, the “lift of r”, which can be expressed in terms of r by universal formulas. The lift of r coincides with the classical limit of the rescaled logarithm of any R-matrix quantizing it