Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of the inverse hull of a 0-left cancellative semigroup   A semigroup S containing a zero element is said to be 0-left cancellative if
st = sr \neq 0 implies that t = r. Given such an S we build an inverse
semigroup H(S), called the inverse hull of S. Motivated by the study of certain
C*-algebras associated to H(S) (a task that we will address in a subsequent
article) we carry out a detailed analysis of the spectrum of the idempotent
semilattice E(S) of H(S) with a special interest in identifying the
ultra-characters. In order to produce examples of characters on E(S), we
introduce the notion of "strings" in a semigroup, attempting to make sense of
the "infinite paths" which are fundamental in the study of graph C*-algebras.
Our strongest results are obtained under the assumption that S admits "least
common multiples", but we also touch upon the notion of "finite alignment",
motivated by the corresponding notion from the theory of higher rank graphs,
and which has also appeared in recent papers by Spielberg and collaborators.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics