The Derived Representation on the Lie Algebra
In this chapter for the first time we begin to deal with the C ∞ or (real) analytic structure of G, rather than with just measure theory. We shall see how a representation of G gives rise to an algebraic representation of the Lie algebra on a dense subspace, for an arbitrary Lie group G. In the case of SL 2(R), this representation has an especially simple form, as shown in §2.
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