Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic structures connected with pairs of compatible associative
  algebras   We study associative multiplications in semi-simple associative algebras over
C compatible with the usual one or, in other words, linear deformations of
semi-simple associative algebras over C. It turns out that these deformations
are in one-to-one correspondence with representations of certain algebraic
structures, which we call M-structures in the matrix case and PM-structures in
the case of direct sums of several matrix algebras. We also investigate various
properties of PM-structures, provide numerous examples and describe an
important class of PM-structures. The classification of these PM-structures
naturally leads to affine Dynkin diagrams of A, D, E-type.

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The categories of this paper are: stat
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
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The categories of this paper are: eess