Lie Algebra Case
An automorphism of a Lie algebra is called an inner automorphism if it is of the form Adg, where Ad is the adjoint map and g is an element of a Lie group whose Lie algebra is . The notion of inner automorphism for Lie algebras is compatible with the notion for groups in the sense that an inner automorphism of a Lie group induces a unique inner automorphism of the corresponding Lie algebra.
Read more about this topic: Inner Automorphism
Famous quotes containing the words lie, algebra and/or case:
“Summoning a child’s voice from a webfoot stone,
Never never oh never to regret the bugle I wore
On my cleaving arm as I blasted in a wave.
Now shown and mostly bare I would lie down,
Lie down, like down and live
As quiet as a bone.”
—Dylan Thomas (1914–1953)
“Poetry has become the higher algebra of metaphors.”
—José Ortega Y Gasset (1883–1955)
“If a playwright tried to see eye to eye with everybody, he would get the worst case of strabismus since Hannibal lost an eye trying to count his nineteen elephants during a snowstorm while crossing the Alps.”
—James Thurber (1894–1961)