Introductory Treatise on Lie's Theory, of Finite Continuous Transformation Groups (Classic Reprint)by John Edward Campbell
In this treatise an attempt is made to give, in as elementary a form as possible, the main outlines of Lie's theory of Continuous Groups. I desire to acknowledge my great indebtedness to Engel's three standard volumes on this subject; they have been constantly before me,
Excerpt from Introductory Treatise on Lie's Theory, of Finite Continuous Transformation Groups
In this treatise an attempt is made to give, in as elementary a form as possible, the main outlines of Lie's theory of Continuous Groups. I desire to acknowledge my great indebtedness to Engel's three standard volumes on this subject; they have been constantly before me, and but for their aid the present work could hardly have been undertaken. His Continuierliche Gruppen, written as it was under Lie's own supervision, must always be referred to for the authoritative exposition of the theory in the form in which Lie left it. During the preparation of this volume I have consulted the several accounts which Scheffers has given of Lie's work in the books entitled Differential-gleichungen, Continuierliche Gruppen, and the Berührungs-Transformationen; and also the interesting sketch of the subject given by Klein in his lectures on Higher Geometry. In addition to these I have read a number of original memoirs, and would specially refer to the writings of Schur in the Mathematische Annalen and in the Leipziger Berichte. Yet, great as are my obligations to others, I am not without hope that even those familiar with the theory of Continuous Groups may find something new in the form in which the theory is here presented. Within the limits of a volume of moderate size the reader will not expect to find an account of all parts of the subject. Thus the theory of the possible types of group-structure has been omitted.
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