Algebras of operators arise frequently in the study of
representations of Lie groups, both finite-dimensional and
infinite-dimensional. This book begins with extensive background
material that covers definitions and terminology, operators in
Hilbert space, and the imprimitivity theorem.
Advancing to considerations of the algebras of operators in Hilbert
space, the heart of the text examines domains of representations,
operators in the enveloping algebra, and spectral theory. The final
section explores covariant representations and connections, with a
particular focus on infinite-dimensional Lie algebras. A helpful
Appendix on the integrability of Lie algebras concludes the text.
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