Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weak Hopf Algebras II: Representation theory, dimensions and the Markov
  trace   If A is a weak C^*-Hopf algebra then the category of finite dimensional
unitary representations of A is a monoidal C^*-category with monoidal unit
being the GNS representation D_eps associated to the counit \eps. This category
has isomorphic left dual and right dual objects which leads, as usual, to the
notion of dimension function. However, if \eps is not pure the dimension
function is matrix valued with rows and columns labelled by the irreducibles
contained in D_eps. This happens precisely when the inclusions A^L < A and A^R
< A are not connected. Still there exists a trace on A which is the Markov
trace for both inclusions. We derive two numerical invariants for each C^*-WHA
of trivial hypercenter. These are the common indices I and \delta, of the Haar,
respectively Markov conditional expectations of either one of the inclusions
A^{L/R} < A and Adual^{L/R} < Adual. In generic cases I > \delta. In the
special case of weak Kac algebras we show that I=\delta is an integer.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th