Editing Simple Lie group (section)

====Notes====
:{{Note|Note†|†}} The group <math>\mathbb{R}</math> is not 'simple' as an abstract group, and according to most (but not all) definitions this is not a simple Lie group. Further, most authors do not count its Lie algebra as a simple Lie algebra. It is listed here so that the list of "irreducible simply connected symmetric spaces" is complete. Note that <math>\mathbb{R}</math> is the only such non-compact symmetric space without a compact dual (although it has a compact quotient ''S''<sup>1</sup>).