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Basic representations of quantum current algebras in higher genus
B. Enriquez, S. Pakuliak, V. Rubtsov
We construct level 1 basic representations of the quantized current algebras associated to higher genus algebraic curves using one free field. We also clarify the relation between…
Coboundary Lie bialgebras and commutative subalgebras of universal enveloping algebras
B. Enriquez, G. Halbout
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 manifold…
On the Drinfeld generators of grt_1(k) and Gamma-functions for associators
B. Enriquez
We prove that the Drinfeld generators of grt_1(k) span the image of this Lie algebra in the abelianization of the commutator of the free Lie algebra with two generators. We show th…
Quantization of some Poisson-Lie dynamical r-matrices and Poisson homogeneous spaces
B. Enriquez, P. Etingof, I. Marshall
Poisson-Lie (PL) dynamical r-matrices are generalizations of dynamical r-matrices, where the base is a Poisson-Lie group. We prove analogues of basic results for these r-matrices,…