In the 1910s the ideas of Lie and Killing were taken up by the French mathematician Élie-Joseph Cartan, who simplified their theory and rederived the classification of what came to be called the classical complex Lie algebras. The simple Lie algebras, out of which all the others in the classification are made, were all representable as algebras of matrices, and, in a sense, Lie algebra is the abstract setting for matrix algebra. Connected to each Lie algebra there were a small number of Lie groups, and there was a canonical simplest one to choose in each case. The groups had ...(100 of 41449 words)