## Representation Theory of Groups and AlgebrasTouching on virtually every important topic in modern representation theory, this book contains proceedings of the activities of the Representation Theory Group at the University of Maryland at College Park during the years 1989-1992. Covered here are the latest results in the field, providing a readable introduction to the work of some of the best young researchers in representation theory. The book spans a very broad spectrum--for example, within real representation theory, both semisimple and nonsemisimple analysis are discussed; within $C^*$-algebras, both geometric and nongeometric approaches are studied. In addition, the articles are exceptionally well written and range from research papers aimed at specialists to expository articles accessible to graduate students. |

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### Contents

Infinitedimensional Lie groups and Lie algebras | 33 |

Quantized differential forms in noncommutative topology and geometry | 65 |

The operator Ktheory | 79 |

Copyright | |

16 other sections not shown

### Common terms and phrases

action acts associated assume automorphism C*-algebra called character classification commutative compact complex condition conjecture connected consider construction contains continuous corresponding decomposition defined definition denote describe determined differential dimension dual element equivalence classes example exists extended fact factor field finite fixed follows formula functions given gives Hence homomorphism identified identity induced integral invariant irreducible isomorphism Langlands lattice Lemma Lie algebra Lie group linear manifold Math Mathematical matrix maximal means measure modules multiplicity natural Note obtain operator orbits pair parameters particular positive problem projection proof Proposition prove pure rank rational forms reductive relation representation respect restriction root satisfying semisimple sequence simple space split structure subgroup Suppose Theorem theory topology trivial unique unital unitary representation universal usual vector write