Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On algebro-geometric Poisson brackets for the Volterra lattice   A generalization of the theory of algebro-geometric Poisson brackets on the
space of finite-gap Schroedinger operators, developped by S. P. Novikov and A.
P. Veselov, to the case of periodic zero-diagonal difference operators of
second order is proposed. A necessary and sufficient condition for such a
bracket to be compatible with higher Volterra flows is found.

20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int