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Essays on representations of real groups Introduction to Lie algebras

This essay is intended to be a self-contained if rather brief introduction to Lie algebras. The first several sections deal with Lie algebras as spaces of invariant vector fields on a Lie group. The very first sections are concerned with different ways to consider vector fields. This early treatment is intended, among other things, to motivate the eventual introduction of abstract Lie algebras, with which all the later sections are concerned.