Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Versions of a Finite-Dimensional Quantum Groupoid   We establish the equivalence of three versions of a finite dimensional
quantum groupoid: a generalized Kac algebra introduced by T. Yamanouchi, a weak
$C^*$-Hopf algebra introduced by G. Bohm, F. Nill and K. Szlachanyi (with an
involutive antipode), and a Kac bimodule -- an algebraic version of a Hopf
bimodule, the notion introduced by J.-M. Vallin. We also study the structure
and construct examples of finite dimensional quantum groupoids.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat