Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Poisson space of bilinear forms with a Poisson Lie action   We consider the space of bilinear forms on a complex N-dimensional vector
space endowed with the quadratic Poisson bracket studied in our previous paper
arXiv:1012.5251. We classify all possible quadratic brackets on the set of
pairs of matrices A and B with the property that the natural action of B on the
defining matrix A of a bilinear form is a Poisson action of a Poisson-Lie
group, thus endowing this space of bilinear forms with the structure of Poisson
homogeneous space. Beside the product Poisson structure we find two more (dual
to each other) structures for which (in contrast to the product Poisson
structure) we can implement the reduction to the space of bilinear forms with
block upper triangular defining matrices by Dirac procedure. We consider the
generalisation of the above construction to triples and show that the space of
bilinear forms then acquires the structure of Poisson symmetric space. We study
also the generalisation to chains of transformations and to the quantum and
quantum affine algebras and the relation between the construction of Poisson
symmetric spaces and that of the Poisson groupoid.

21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat