Lecture Notes in Mathematics

Algebraic Groups and Lie Groups with Few Factors

Authors: Di Bartolo, A., Falcone, G., Plaumann, P., Strambach, K.

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About this book

Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular, the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three-dimensional unipotent algebraic groups over a perfect field of positive characteristic, as well as, by many concrete examples which cover an area systematically. In the final section, algebraic groups and Lie groups having many closed normal subgroups are determined.

Reviews

From the reviews:

"This is a self-contained carefully written lecture note on algebraic groups as well as real and complex Lie groups. For algebraic groups the authors stress the difference between groups over fields of characteristic zero and characteristic p. … Overall the notes provide an excellent introduction to the subject and this research monograph presents remarkable and powerful results. It is a good reference for researchers working on groups outside the family of reductive groups." (Jorge A. Vargas, Mathematical Reviews, Issue 2009 g)

“The authors study both algebraic groups and real and complex Lie groups by imposing on their connected subgroups the analogues of familiar conditions in abstract group theory. … This book serves as a valuable resource to those working in the field of algebraic groups and as a good place to learn about this aspect of that field.” (Ernest L. Stitzinger, Zentralblatt MATH, Vol. 1176, 2010)


Table of contents (7 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-78584-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-78583-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Groups and Lie Groups with Few Factors
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1944
Copyright
2008
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-78584-2
DOI
10.1007/978-3-540-78584-2
Softcover ISBN
978-3-540-78583-5
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVI, 212
Topics