Simple Lie Groups
Unfortunately there is no generally accepted definition of a simple Lie group, and in particular it is not necessarily defined as a Lie group that is simple as an abstract group. Authors differ on whether a simple Lie group has to be connected, or on whether it is allowed to have a non-trivial center, or on whether R is a simple Lie group.
The most common definition implies that simple Lie groups must be connected, and non-abelian, but are allowed to have a non-trivial center.
In this article the connected simple Lie groups with trivial center are listed. Once these are known, the ones with non-trivial center are easy to list as follows. Any simple Lie group with trivial center has a universal cover, whose center is the fundamental group of the simple Lie group. The corresponding simple Lie groups with non-trivial center can be obtained as quotients of this universal cover by a subgroup of the center.
Read more about this topic: List Of Simple Lie Groups
Famous quotes containing the words simple, lie and/or groups:
“Our whole walk was through a thoroughly Catholic country, and there was no trace of any other religion. I doubt if there are any more simple and unsophisticated Catholics anywhere.”
—Henry David Thoreau (1817–1862)
“America is, therefore the land of the future, where, in the ages that lie before us, the burden of the World’s history shall reveal itself. It is a land of desire for all those who are weary of the historical lumber-room of Old Europe.”
—Georg Wilhelm Friedrich Hegel (1770–1831)
“Trees appeared in groups and singly, revolving coolly and blandly, displaying the latest fashions. The blue dampness of a ravine. A memory of love, disguised as a meadow. Wispy clouds—the greyhounds of heaven.”
—Vladimir Nabokov (1899–1977)