In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. A great deal is known about such representations, a basic tool in their study being the use of the corresponding 'infinitesimal' representations of Lie algebras. The physics literature sometimes passes over the distinction between Lie group representations and Lie algebra representations.
Read more about Representation Of A Lie Group: Representations On A Complex Finite-dimensional Vector Space, Representations On A Finite-dimensional Vector Space Over An Arbitrary Field, Representations On Hilbert Spaces, Classification, Formulaic Examples
Famous quotes containing the words representation of, lie and/or group:
“All great amusements are dangerous to the Christian life; but among all those which the world has invented there is none more to be feared than the theater. It is a representation of the passions so natural and so delicate that it excites them and gives birth to them in our hearts, and, above all, to that of love.”
—Blaise Pascal (1623–1662)
“The lesson which these observations convey is, be, and not seem. Let us acquiesce. Let us take our bloated nothingness out of the path of the divine circuits. Let us unlearn our wisdom of the world. Let us lie low in the lord’s power, and learn that truth alone makes rich and great.”
—Ralph Waldo Emerson (1803–1882)
“The boys think they can all be athletes, and the girls think they can all be singers. That’s the way to fame and success. ...as a group blacks must give up their illusions.”
—Kristin Hunter (b. 1931)