On Weitzenböck's theorem in positive characteristic
Author:
A. Fauntleroy
Journal:
Proc. Amer. Math. Soc. 64 (1977), 209213
MSC:
Primary 14L99
MathSciNet review:
0460345
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Abstract: Let k be an algebraically closed field and let be a finitedimensional krational representation of the additive group . If the subspace of fixed points in V is a hyperplane, then the ring of 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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 A. Borel, Linear representations of semisimple algebraic groups, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R. I., 1975, pp. 421440. MR 0372054 (51:8271)
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 M. Hochster and J. Roberts, Rings of invariants of reductive groups acting on regular rings are CohenMacaulay, Advances in Math. 13 (1974), 115175. MR 0347810 (50:311)
 [4]
 T. Kambayashi, M. Miyanishi and M. Takeuchi, Unipotent algebraic groups, Lecture Notes in Math., vol. 414, SpringerVerlag, Berlin and New York, 1974. MR 0376696 (51:12871)
 [5]
 O. Ore, On a special class of polynomials, Trans. Amer. Math. Soc. 35 (1933), 559584. MR 1501703
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 C. S. Seshadri, On a theorem of Weitzenböck, J. Math. Kyoto 13 (1962).
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 Samuel Zariski, Commutative algebra, Vol. I, Van Nostrand, Princeton, N. J., 1960. MR 0120249 (22:11006)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197704603453
PII:
S 00029939(1977)04603453
Keywords:
actions,
ring of invariants
Article copyright:
© Copyright 1977
American Mathematical Society
