Categories of Symmetries and Infinite-dimensional Groups

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Clarendon Press, 1996 - Mathematics - 417 pages
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For mathematicians working in group theory, the study of the many infinite-dimensional groups has been carried out in an individual and non-coherent way. For the first time, these apparently disparate groups have been placed together, in order to construct the `big picture'. This booksuccessfully gives an account of this - and shows how such seemingly dissimilar types such as the various groups of operators on Hilbert spaces, or current groups are shown to belong to a bigger entitity. This is a ground-breaking text will be important reading for advanced undergraduate andgraduate mathematicians.
 

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Contents

Spinor representation
17
Representations of the complex classical categories
68
Fermion Fock space
100
finite dimensional case
126
infinitedimensional case
157
Representations of the group of diffeomorphisms of
202
group
212
The heavy groups
250
g Infinitedimensional classical groups and almostinvariant
293
Some algebraic constructions of measure theory
342
The real classical categories
373
Bosonfermion correspondence
382
Characteristic LivSic function
388
References
398
Index
415
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About the author (1996)

Yu A. Neretin is at the Institute of Electronic Machine Building, Moscow, Bolshoi .

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