Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ideals in the Goldman Algebra   The goal of this work is to study the ideals of the Goldman Lie algebra $S$.
To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic
structure, and focus on finding ideals of this new structure instead. The
structure $S$ can be regarded as either a $\mathbb{Q}$-module or a
$\mathbb{Q}$-module generated by free homotopy classes. For $\mathbb{Z}$-module
case, we proved that there is an infinite class of ideals of $S$ that contain a
certain finite set of free homotopy classes. For $\mathbb{Q}$-module case, we
can classify all the ideals of the new structure and consequently obtain a new
class of ideals of the original structure. Finally, we show an interesting
infinite chain of ideals that are not those ideals obtained by considering the
new structure.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org