Encyclopaedia of Mathematical Sciences

Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action

Authors: Bialynicki-Birula, A., Carrell, J., McGovern, W.M.

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About this book

This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on algebraic varieties, giving a detailed exposition of many of the cohomological results one obtains from having a torus action with fixed points. Many examples, such as toric varieties and flag varieties, are discussed in detail. W.M. McGovern studies the actions of a semisimple Lie or algebraic group on its Lie algebra via the adjoint action and on itself via conjugation. His contribution focuses primarily on nilpotent orbits that have found the widest application to representation theory in the last thirty-five years.

Reviews

"This volume of the Encyclopaedia of Mathematical Sciences contains three contributions on actions of algebraic groups. The first one, by A. Bialynicki-Birula, is concerned with the general concept of a quotient, while the other two, by J.B.Carrell and W.M. McGovern, are on more specific topics. [...]

These three articles are all of value, but have somewhat different nature. Bialynicki-Birula's is a survey of a very wide area of research and requires much prior knowledge on the part of the reader. It is certainly not some something one could suggest as reading for a starting graduate student, but it is a useful reference for those who already have some knowledge and want to know about some aspect of the theory of quotients. The other two articles are much more accessible, especially that of McGovern, but could also be used as a source of general reference in the (more limited) areas they study."

P.Newstead, Liverpool, Jahresberichte der DMV, Vol. 107, Issue 4 (2005)


Table of contents (3 chapters)

  • Quotients by Actions of Groups

    BiaƂynicki-Birula, Andrzej

    Pages 1-82

  • Torus Actions and Cohomology

    Carrell, James B.

    Pages 83-158

  • The Adjoint Representation and the Adjoint Action

    McGovern, William M.

    Pages 159-238

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-662-05071-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-540-43211-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $159.00
price for USA
  • ISBN 978-3-642-07745-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Quotients. Torus Actions and Cohomology. The Adjoint Representation and the Adjoint Action
Authors
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
131
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-05071-2
DOI
10.1007/978-3-662-05071-2
Hardcover ISBN
978-3-540-43211-1
Softcover ISBN
978-3-642-07745-6
Series ISSN
0938-0396
Edition Number
1
Number of Pages
V, 242
Topics