CHAPTER 15

Lie Groups

15.1. Lie Groups, Invariant Vector Fields and Forms

Is the unitary group *SU* (*n*) connected?

15.1a. Lie Groups

Let *M*(*n × n*) be the set of all *n × n* real matrices. As in Section 1.1d, we shall associate to the matrix *x* the point in *n*^{2}-dimensional euclidean space whose coordinates are *x*_{11}, *x*_{12},…, *x _{nn}*. Topologically then,

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