Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursion and Hamiltonian operators for integrable nonabelian difference
  equations   In this paper, we carry out the algebraic study of integrable
differential-difference equations whose field variables take values in an
associative (but not commutative) algebra. We adapt the Hamiltonian formalism
to nonabelian difference Laurent polynomials and describe how to obtain a
recursion operator from the Lax representation of an integrable nonabelian
differential-difference system. As an application, we propose a novel family of
integrable equations: the nonabelian Narita-Itoh-Bogoyavlensky lattice, for
which we construct their recursion operators and Hamiltonian operators and
prove the locality of infinitely many commuting symmetries generated from their
highly nonlocal recursion operators. Finally, we discuss the nonabelian version
of several integrable difference systems, including the relativistic Toda chain
and Ablowitz-Ladik lattice.

12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex