Varieties of representations of finitely generated groups / Alexander Lubotzky and Andy R. Magid.

Author
Lubotzky, Alexander, 1956- [Browse]
Format
Book
Language
English
Published/​Created
Providence, R.I., USA : American Mathematical Society, ©1985.
Description
xi, 117 pages : illustrations ; 26 cm.

Details

Subject(s)
Series
Summary note
The n-dimensional representations, over an algebraically closed characteristic zero field k, of a finitely generated group are parameterized by an affine algebraic variety over k. The tangent spaces of this variety are subspaces of spaces of one-cocycles and thus the geometry of the variety is locally related to the cohomology of the group. The cohomology is also related to the prounipotent radical of the proalgebraic hull of the group. This paper exploits these two relations to compute dimensions of representation varieties, especially for nilpotent groups and their generalizations. It also presents the foundations of the theory of representation varieties in an expository, self-contained manner.
Notes
"November 1985, Volume 58, number 336 (second of four numbers)."
Bibliographic references
Bibliography: p. 114-117.
Contents
  • Schemes and varieties of representations
  • Tangent spaces and first cohomology
  • Cohomology and Fox derivatives
  • Cohomology and the proalgebraic hull
  • The character twisting operation
  • Representation varieties of nilpotent groups
  • Historical remarks
  • References.
ISBN
  • 082182337X ((pbk. ; : alk. paper))
  • 9780821823378 ((pbk. ; : alk. paper))
LCCN
85021444
OCLC
12721103
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