Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Theory of Dimension   In which a theory of dimension related to the Jones index and based on the
notion of conjugation is developed. An elementary proof of the additivity and
multiplicativity of the dimension is given and there is an associated trace.
Applications are given to a class of endomorphisms of factors and to the theory
of subfactors. An important role is played by a notion of amenability inspired
by the work of Popa.

19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph