Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path algebras and monomial algebras of finite GK-dimension as
  noncommutative homogeneous coordinate rings   This article sets out to understand the categories $\QGr A$ where $A$ is
either a monomial algebra or a path algebra of finite Gelfand-Kirillov
dimension. The principle questions are: 1) What is the structure of the point
modules up to isomorphism in $\QGr A$? 2) When is $\QGr A \equiv \QGr A'$?
These two questions turn out to be intimately related.
  It is shown that up to isomorphism in $\QGr A$, there are only finitely many
point modules and these give all the simple objects in the category. Then, a
finite quiver $E_A$, which can be constructed from the algebra $A$ rather
simply, is associated to the category $\QGr A$. It is shown that the vertices
of $E_A$ are in bijection with the point modules and the arrows are determined
by the extensions between point modules. Lastly, it is shown that $\QGr A\equiv
\QGr A'$ if and only if $E_A=E_{A'}$.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph