Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A classification of Curtis-Tits amalgams   A celebrated theorem of Curtis and Tits on groups with finite BN-pair shows
that roughly speaking these groups are determined by their local structure.
This result was later extended to Kac-Moody groups by P.~Abramenko and
B.~M\"uhlherr. Their theorem states that a Kac-Moody group $G$ is the universal
completion of an amalgam of rank two (Levi) subgroups, as they are arranged
inside $G$ itself.
  Taking this result as a starting point, we define a Curtis-Tits structure
over a given diagram to be an amalgam of groups such that the sub-amalgam
corresponding to a two-vertex sub-diagram is the Curtis-Tits amalgam of some
rank-$2$ group of Lie type. There is no a priori reference to an ambient group,
nor to the existence of an associated (twin-) building. Indeed, there is no a
priori guarantee that the amalgam will not collapse. We then classify these
amalgams up to isomorphism.
  In the present paper we consider triangle-free simply-laced diagrams. Instead
of using Goldschmidt's lemma, we introduce a new approach by applying Bass and
Serre's theory of graphs of groups. The classification reveals a natural
division into two main types: "orientable" and "non-orientable" Curtis-Tits
structures. Our classification of orientable Curtis-Tits structures naturally
fits with the classification of all locally split Kac-Moody groups using
Moufang foundations. In particular, our classification yields a simple
criterion for recognizing when Curtis-Tits structures give rise to Kac-Moody
groups. The class of non-orientable Curtis-Tits structures is in some sense
much larger. Many of these amalgams turn out to have non-trivial interesting
completions inviting further study.

8
The categories of this paper are: hep-ex
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th