Grundlehren der mathematischen Wissenschaften

The Classical Groups and K-Theory

Authors: Hahn, Alexander, O'Meara, O.Timothy

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About this book

It is a great satisfaction for a mathematician to witness the growth and expansion of a theory in which he has taken some part during its early years. When H. Weyl coined the words "classical groups", foremost in his mind were their connections with invariant theory, which his famous book helped to revive. Although his approach in that book was deliberately algebraic, his interest in these groups directly derived from his pioneering study of the special case in which the scalars are real or complex numbers, where for the first time he injected Topology into Lie theory. But ever since the definition of Lie groups, the analogy between simple classical groups over finite fields and simple classical groups over IR or C had been observed, even if the concept of "simplicity" was not quite the same in both cases. With the discovery of the exceptional simple complex Lie algebras by Killing and E. Cartan, it was natural to look for corresponding groups over finite fields, and already around 1900 this was done by Dickson for the exceptional Lie algebras G and E • However, a deep reason for this 2 6 parallelism was missing, and it is only Chevalley who, in 1955 and 1961, discovered that to each complex simple Lie algebra corresponds, by a uniform process, a group scheme (fj over the ring Z of integers, from which, for any field K, could be derived a group (fj(K).

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Buy this book

eBook $159.00 net
( price for USA )
  • ISBN 978-3-662-13152-7
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Hardcover $209.00 net
( price for USA )
  • ISBN 978-3-540-17758-6
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days
Softcover $209.00 net
( price for USA )
  • ISBN 978-3-642-05737-3
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
The Classical Groups and K-Theory
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
291
Copyright
1989
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-13152-7
DOI
10.1007/978-3-662-13152-7
Hardcover ISBN
978-3-540-17758-6
Softcover ISBN
978-3-642-05737-3
Series ISSN
0072-7830
Edition Number
1
Topics