In this section some facts are collected on the structure theory of Lie groups and Lie algebras. We will be brief and almost no proofs will be given. For more details and proofs, see the books by Adams , Helgason , and Varadarajan . For most purposes, the paper by Howe  treats Lie groups in an elementary way and provides the basic facts required for this book. We will not need too much “high technology”, and the reader is safe if he keeps thinking of SL(2, ℝ) and its Lie algebra sl(2, R) (to be defined later). The advanced reader may skip this chapter.
KeywordsUnitary Representation Haar Measure Polynomial Growth Maximal Compact Subgroup Irreducible Unitary Representation
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