Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quasi-Coxeter categories and a relative Etingof-Kazhdan quantization
  functor   Let g be a symmetrizable Kac-Moody algebra and U_h(g) its quantized
enveloping algebra. The quantum Weyl group operators of U_h(g) and the
universal R-matrices of its Levi subalgebras endow U_h(g) with a natural
quasi-Coxeter quasitriangular quasibialgebra structure which underlies the
action of the braid group of g and Artin's braid groups on the tensor product
of integrable, category O modules. We show that this structure can be
transferred to the universal enveloping algebra Ug[[h]]. The proof relies on a
modification of the Etingof-Kazhdan quantization functor, and yields an
isomorphism between (appropriate completions of) U_h(g) and Ug[[h]] preserving
a given chain of Levi subalgebras. We carry it out in the more general context
of chains of Manin triples, and obtain in particular a relative version of the
Etingof-Kazhdan functor with input a split pair of Lie bialgebras. Along the
way, we develop the notion of quasi-Coxeter categories, which are to
generalized braid groups what braided tensor categories are to Artin's braid
groups. This leads to their succint description as a 2-functor from a
2-category whose morphisms are De Concini-Procesi associahedra. These results
will be used in the sequel to this paper to give a monodromic description of
the quantum Weyl group operators of an affine Kac-Moody algebra, extending the
one obtained by the second author for a semisimple Lie algebra.

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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an