Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized q-Onsager algebras and boundary affine Toda field theories   Generalizations of the q-Onsager algebra are introduced and studied. In one
of the simplest case and q=1, the algebra reduces to the one proposed by
Uglov-Ivanov. In the general case and $q\neq 1$, an explicit algebra
homomorphism associated with coideal subalgebras of quantum affine Lie algebras
(simply and non-simply laced) is exhibited. Boundary (soliton non-preserving)
integrable quantum Toda field theories are then considered in light of these
results. For the first time, all defining relations for the underlying
non-Abelian symmetry algebra are explicitely obtained. As a consequence, based
on purely algebraic arguments all integrable (fixed or dynamical) boundary
conditions are classified.

11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom