Elements Of Mathematics: Lie Groups And Lie Algebras Chapters 1-3

This is the softcover reprint of the English translation of 1975 (available from Springer since 1989) of the first 3 chapters of Bourbaki's 'Groupes et algA]bres de Lie'. The first chapter describes the theory of Lie algebras, their derivations, their representations and their enveloping algebras. In Ch. 2, free Lie algebras are introduced in order to discuss the exponential, logarithmic and the Hausdorff series. Ch. 3 deals with the theory of Lie groups over R and C and ultrametric fields. It describes the connections between their local and global properties, and the properties of their Lie algebras. It is one of the very best references on this subject.