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 | References | Similar Articles | Additional Information

Abstract: Let *k* be an algebraically closed field and let be a finite-dimensional *k*-rational 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.

**[1]**A. Borel,*Linear representations of semi-simple algebraic groups*, Proc. Sympos. Pure Math., vol. 29, Amer. Math. Soc., Providence, R. I., 1975, pp. 421-440. MR**0372054 (51:8271)****[2]**A. Fauntleroy,*Linear*-*actions on affine spaces and associated rings of invariants*, J. Pure Appl. Algebra**9**(1977). MR**0447268 (56:5583)****[3]**M. Hochster and J. Roberts,*Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay*, Advances in Math.**13**(1974), 115-175. MR**0347810 (50:311)****[4]**T. Kambayashi, M. Miyanishi and M. Takeuchi,*Unipotent algebraic groups*, Lecture Notes in Math., vol. 414, Springer-Verlag, Berlin and New York, 1974. MR**0376696 (51:12871)****[5]**O. Ore,*On a special class of polynomials*, Trans. Amer. Math. Soc.**35**(1933), 559-584. MR**1501703****[6]**C. S. Seshadri,*On a theorem of Weitzenböck*, J. Math. Kyoto**1-3**(1962).**[7]**Samuel Zariski,*Commutative algebra*, Vol. I, Van Nostrand, Princeton, N. J., 1960. MR**0120249 (22:11006)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1977-0460345-3

Keywords:
-actions,
ring of invariants

Article copyright:
© Copyright 1977
American Mathematical Society