Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unbounded strongly irreducible operators and transitive representations
  of quivers on infinite-dimensional Hilbert spaces   We introduce unbounded strongly irreducible operators and transitive
operators. These operators are related to a certain class of indecomposable
Hilbert representations of quivers on infinite-dimensional Hilbert spaces. We
regard the theory of Hilbert representations of quivers is a generalization of
the theory of unbounded operators. A non-zero Hilbert representation of a
quiver is said to be transitive if the endomorphism algebra is trivial. If a
Hilbert representation of a quiver is transitive, then it is indecomposable.
But the converse is not true. Let $\Gamma$ be a quiver whose underlying
undirected graph is an extended Dynkin diagram. Then there exists an
infinite-dimensional transitive Hilbert representation of $\Gamma$ if and only
if $\Gamma$ is not an oriented cyclic quiver.

19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin