Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Abelian ideals of a Borel subalgebra and root systems, II   Let $\mathfrak g$ be a simple Lie algebra with a Borel subalgebra $\mathfrak
b$ and $\mathfrak{Ab}$ the set of abelian ideals of $\mathfrak b$. Let
$\Delta^+$ be the corresponding set of positive roots. We continue our study of
combinatorial properties of the partition of $\mathfrak{Ab}$ parameterised by
the long positive roots. In particular, the union of an arbitrary set of
maximal abelian ideals is described, if $\mathfrak g\ne\mathfrak{sl}_n$. We
also characterise the greatest lower bound of two positive roots, when it
exists, and point out interesting subposets of $\Delta^+$ that are modular
lattices.

5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics