Lie Algebra Of Local Killing Fields

INTRODUCTION TO DIFFERENTIAL GEOMETRY

The last section uses these results to show that the Killing form on a simple Lie algebra is nondegenerate, to establish uniqueness up to conjugation of maximal compact subgroups of the automorphism group of a semisimple Lie algebra, and to prove Cartan’s theorem about the compact real form of a semisimple complex Lie algebra.

  Introduction, Differential, Killing, Geometry, Algebra, Lie algebras, Introduction to differential geometry

Geometric Models for Noncommutative Algebras

Geometric Models for Noncommutative Algebras Ana Cannas da Silva1 Alan Weinstein2 University of California at Berkeley December 1, 1998 1acannas@math.berkeley.edu, acannas@math.ist.utl.pt 2alanw@math.berkeley.edu