1,947 research outputs found
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
Poisson algebras associated to quasi-Hopf algebras
We define admissible quasi-Hopf quantized universal enveloping (QHQUE)
algebras by h-adic valuation conditions. We show that any QHQUE algebra is
twist-equivalent to an admissible one. We prove a related statement: any
associator is twist-equivalent to a Lie associator. We attach a quantized
formal series algebra to each admissible QHQUE algebra and study the resulting
Poisson algebras.Comment: We construct a lift for any Lie quasi-bialgebra with zero cobracke
SOS model partition function and the elliptic weight functions
We generalize a recent observation [arXiv:math/0610433] that the partition
function of the 6-vertex model with domain-wall boundary conditions can be
obtained by computing the projections of the product of the total currents in
the quantum affine algebra in its current
realization. A generalization is proved for the the elliptic current algebra
[arXiv:q-alg/9703018,arXiv:q-alg/9601022]. The projections of the product of
total currents are calculated explicitly and are represented as integral
transforms of the product of the total currents. We prove that the kernel of
this transform is proportional to the partition function of the SOS model with
domain-wall boundary conditions.Comment: 21 pages, 5 figures, requires iopart packag
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