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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On Weitzenböck’s theorem in positive characteristic


Author: A. Fauntleroy
Journal: Proc. Amer. Math. Soc. 64 (1977), 209-213
MSC: Primary 14L99
DOI: https://doi.org/10.1090/S0002-9939-1977-0460345-3
MathSciNet review: 0460345
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Abstract: Let k be an algebraically closed field and let $f:{G_a} \to {\text {GL}}(V)$ be a finite-dimensional k-rational representation of the additive group ${G_a}$. If the subspace of ${G_a}$-fixed points in V is a hyperplane, then the ring of ${G_a}$-invariant polynomial functions on V is finitely generated over k. This result is an analog of a classical theorem of Weitzenböck, a modern proof of which has been given by C. S. Seshadri.


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Keywords: <IMG WIDTH="31" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${G_a}$">-actions, ring of invariants
Article copyright: © Copyright 1977 American Mathematical Society