Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite dimensional representations of finite dimensional algebras and
  amenability   We present a novel approach to the representation theory of finite
dimensional algebras motivated by the emerging theory of graph limits.
  We introduce the rank spectrum of a finite dimensional algebra $R$ over a
finite field. The elements of the rank spectrum are representations of the
algebra into von Neumann regular rank algebras, and two representations are
considered to be equivalent if they induce the same Sylvester rank functions on
$R$-matrices.
  Based on this approach, we can divide the finite dimensional algebras into
three types: finite, amenable and non-amenable representation types. We prove
that string algebras are of amenable representation type, but the wild
Kronecker algebras are not. Here, the amenability of the rank algebras
associated to the limit points in the rank spectrum plays a very important
part.
  We also show that the limit points of finite dimensional representations of
algebras of amenable representation type can always be viewed as
representations of the algebra in the continuous ring invented by John von
Neumann in the 1930's.
  As an application in algorithm theory, we introduce and study the notion of
testing of parameters of modules over finite dimensional algebras, that is
analogous to the property testing of bounded degree graphs introduced by
Goldreich and Ron. We shall see that for string algebras all the reasonable
(stable) parameters are testable.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th