Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Affine connections, duality and divergences for a von Neumann algebra   On the predual of a von Neumann algebra, we define a differentiable manifold
structure and affine connections by embeddings into non-commutative L_p-spaces.
Using the geometry of uniformly convex Banach spaces and duality of the L_p and
L_q spaces for 1/p+1/q=1, we show that we can introduce the \alpha-divergence,
for \alpha in (-1,1), in a similar manner as Amari in the classical case. If
restricted to the positive cone, the \alpha-divergence belongs to the class of
quasi-entropies, defined by Petz.

13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess