Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphs, Frobenius functionals, and the classical Yang-Baxter equation   A Lie algebra is Frobenius if it admits a linear functional F such that the
Kirillov form F([x,y]) is non-degenerate. If g is the m-th maximal parabolic
subalgebra P(n,m) of sl(n) this occurs precisely when (n,m) = 1. We define a
"cyclic" functional F on P(n,m) and prove it is non-degenerate using properties
of certain graphs associated to F. These graphs also provide in some cases
readily computable associated solutions of the classical Yang-Baxter equation.
We also define a local ring associated to each connected loopless graph from
which we show that the graph can be reconstructed. Finally, we examine the
seaweed Lie algebras of Dergachev and Kirillov from our perspective.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas