Pure Picard-Vessiot extensions with generic properties

Author:
Lourdes Juan

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2549-2556

MSC (2000):
Primary 12H05; Secondary 12F12, 20G15

DOI:
https://doi.org/10.1090/S0002-9939-04-07390-3

Published electronically:
April 8, 2004

MathSciNet review:
2054779

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a connected linear algebraic group over an algebraically closed field of characteristic 0, we construct a pure Picard-Vessiot extension for , namely, a Picard-Vessiot extension , with differential Galois group , such that and are purely differentially transcendental over . The differential field is the quotient field of a -stable proper differential subring with the property that if is any differential field with field of constants and is a Picard-Vessiot extension with differential Galois group a connected subgroup of , then there is a differential homomorphism such that is generated over as a differential field by .

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Additional Information

**Lourdes Juan**

Affiliation:
Department of Mathematics and Statistics, Texas Tech University, Box 41042, Lubbock, Texas 79409-1042

Email:
ljuan@math.ttu.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07390-3

Received by editor(s):
August 26, 2002

Received by editor(s) in revised form:
June 2, 2003

Published electronically:
April 8, 2004

Additional Notes:
The author was supported in part by NSA grant No. MDA904-02-1-0084

Communicated by:
Lance W. Small

Article copyright:
© Copyright 2004
American Mathematical Society