Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantization of a Poisson structure on products of principal affine
  spaces   We give the analogue for Hopf algebras of the polyuble Lie bialgebra
construction by Fock and Rosli. By applying this construction to the
Drinfeld-Jimbo quantum group, we obtain a deformation quantization
$\mathbb{C}_\hslash[(N \backslash G)^m]$ of a Poisson structure $\pi^{(m)}$ on
products $(N \backslash G)^m$ of principal affine spaces of a connected and
simply connected complex semisimple Lie group $G$. The Poisson structure
$\pi^{(m)}$ descends to a Poisson structure $\pi_m$ on products $(B \backslash
G)^m$ of the flag variety of $G$ which was introduced and studied by the Lu and
the author. Any ample line bundle on $(B \backslash G)^m$ inherits a natural
flat Poisson connection, and the corresponding graded Poisson algebra is
quantized to a subalgebra of $\mathbb{C}_\hslash[(N \backslash G)^m]$.
  We define the notion of a strongly coisotropic subalgebra in a Hopf algebra,
and explain how strong coisotropicity guarantees that any homogeneous
coordinate ring of a homogeneous space of a Poisson Lie group can be quantized
in the sense of Ciccoli, Fioresi, and Gavarini.

0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an