Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $ R $--matrix action of untwisted affine quantum groups at roots of
  1   Let $\hat{\frak g}$ be an untwisted affine Kac-Moody algebra. The quantum
group $U_h(\hat{\frak g})$ (over $\mathbb{C}[[h]]$) is known to be a
quasitriangular Hopf algebra: in particular, it has a universal $ R $--matrix,
which yields an $ R $--matrix for each pair of representations of
$U_h(\hat{\frak g})$. On the other hand, the quantum group $U_q(\hat{\frak g})$
(over $\mathbb{C}(q) $) also has an $ R $--matrix for each pair of
representations, but it has not a universal $ R $--matrix so that one cannot
say that it is quasitriangular. Following Reshetikin, one introduces the
(weaker) notion of braided Hopf algebra: then $ U_q(\hat{\frak g})$ is a
braided Hopf algebra.
  In this work we prove that also the unrestricted specializations of
$U_q(\hat{\frak g})$ at roots of 1 are braided: in particular, specializing $q$
at 1 we have that the function algebra $F \big[ \hat{H} \big]$ of the Poisson
proalgebraic group $\hat{H}$ dual of $\hat{G}$ (a Kac-Moody group with Lie
algebra $\hat{\frak g} \,$) is braided. This is useful because, despite these
specialized quantum groups are not quasitriangular, the braiding is enough for
applications, mainly for producing knot invariants. As an example, the action
of the $ R $--matrix on (tensor products of) Verma modules can be specialized
at odd roots of 1.

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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: cs
10
The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph