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
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