Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zinbiel algebras and bialgebras: main properties and related algebraic
  structures   This work provides a characterization of left and right Zinbiel
algebras.Basic identities are established and discussed, showing that Zinbiel
algebras are center-symmetric, and therefore Lie-admissible algebras. Their
bimodules are given, and used to build a Zinbiel algebra structure on the
direct sum of the underlying vector space and a finite-dimensional vector
space. In addition, their matched pair is built, and related to the matched
pair of their sub-adjacent Lie algebras. Besides, Zinbiel coalgebras are
introduced, and linked to their underlying Lie coalgebras and coassociative
coalgebras. Moreover, the related Manin triple is defined, and used to
characterize Zinbiel bialgebras, and their equivalence to the associated
matched pair.

26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex