Lie Group

The theory of Lie groups rests on three pillars: analysis topology and algebra. Correspondingly it is possible to distinguish several phases overlapping in some degree in its development. It also allows one to regard the subject from different points of view and it is the algebraic standpoint which has been chosen in this tract as the most suitable one for a first introduction to the subject. The aim has been to develop the beginnings of the theory of Lie groups especially the fundamental theorems of Lie relating the group to its infinitesimal generators (the Lie algebra); this account occupies the first five chapters. Next to Lie''s theorems in importance come the basic properties of subgroups and homomorphisms and they form the content of Chapter VI. The final chapter on the universal covering group could perhaps be most easily dispensed with but it is hoped justifies its existence by bringing back into circulation Schreier''s elegant method of constructing covering groups.