Lower bounds for dimensions of

representation varieties

Author:
Andy R. Magid

Journal:
Trans. Amer. Math. Soc. **350** (1998), 4609-4621

MSC (1991):
Primary 20C15

DOI:
https://doi.org/10.1090/S0002-9947-98-01996-5

MathSciNet review:
1433124

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Abstract | References | Similar Articles | Additional Information

Abstract: The set of -dimensional complex representations of a finitely generated group form a complex affine variety . Suppose that is such a representation and consider the associated representation on complex matrices obtained by following with conjugation of matrices. Then it is shown that the dimension of at is at least the difference of the complex dimensions of and . It is further shown that in the latter cohomology may be replaced by various proalgebraic groups associated to and .

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Additional Information

**Andy R. Magid**

Affiliation:
Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019

Email:
amagid@ou.edu

DOI:
https://doi.org/10.1090/S0002-9947-98-01996-5

Keywords:
Finitely generated roups,
linear representations,
varieties,
cohomolgy

Received by editor(s):
May 25, 1995

Received by editor(s) in revised form:
November 25, 1996

Additional Notes:
Partially supported by NSA grant MDA904–92–H–3038

Article copyright:
© Copyright 1998
American Mathematical Society