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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Triangular $G_{a}$ actions on $\mathbf{C}^{4}$


Authors: James K. Deveney, David R. Finston and Peter van Rossum
Journal: Proc. Amer. Math. Soc. 132 (2004), 2841-2848
MSC (2000): Primary 14L30; Secondary 20G20
Published electronically: June 2, 2004
MathSciNet review: 2063101
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Abstract: Every locally trivial action of the additive group of complex numbers on four-dimensional complex affine space that is given by a triangular derivation is conjugate to a translation. A criterion for a proper action on complex affine $n$-space to be locally trivial is given, along with an example showing that the hypotheses of the criterion are sharp.


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Additional Information

James K. Deveney
Affiliation: Department of Mathematical Sciences, Virginia Commonwealth University, 1015 W. Main St., Richmond, Virginia 23284
Email: jdeveney@atlas.vcu.edu

David R. Finston
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email: dfinston@nmsu.edu

Peter van Rossum
Affiliation: Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003
Email: petervr@nmsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07500-8
PII: S 0002-9939(04)07500-8
Keywords: Additive group, slice, geometric quotient, locally trivial
Received by editor(s): July 25, 2002
Published electronically: June 2, 2004
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society