Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rota-Baxter systems on Hom-associative algebras and covariant
  Hom-bialgebras   Rota-Baxter systems were introduced by Brzezi\'{n}ski as a generalization of
Rota-Baxter operators that are related to dendriform structures, associative
Yang-Baxter pairs and covariant bialgebras. In this paper, we define
Rota-Baxter systems on Hom-associative algebras and show how they induce
Hom-dendriform structures and weak pseudotwistors on the underlying
Hom-associative algebra. We introduce Hom-Yang-Baxter pairs and a notion of
covariant Hom-bialgebra. Given a Hom-Yang-Baxter pair, we construct a twisted
Rota-Baxter system and a (quasitriangular) covariant Hom-bialgebra. Finally, we
consider perturbations of the coproduct in a covariant Hom-bialgebra.

32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin