Lie Groups and Lie Algebras

Abstract

In various fields of geometry and applications object that simultaneously carry the structure of a group and a structure of a smooth manifold occur. These objects are called Lie groups provided that the group operations are smooth. As a rule, Lie groups that occur in applications have nontrivial topological structure. In the introduction to this chapter we will consider one such example, the group SO(3) of orthogonal matrices of size 3 × 3 with the determinant equal to one.