Unfortunately there is no single standard definition of a simple Lie group.

Further examples can be found in the table of Lie groups.

This is a significant result, as other Lie groups lead to different normalizations.

They are the smallest of the five exceptional simple Lie groups.

It's easy to extend the results to the Lie group.

He published his first book, on Lie groups, in 1957.

The Lie group acts on the vector space in a natural way.

Other techniques specific to Lie groups are used as well.

In particular, this has an application to the classification of Lie groups.

The notion of a real form can also be defined for complex Lie groups.