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]**Armand Borel,*Linear representations of semi-simple algebraic groups*, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974) Amer. Math. Soc., Providence, R.I., 1975, pp. 421–440. MR**0372054****[2]**Amassa Fauntleroy,*Linear 𝐺ₐ actions on affine spaces and associated rings of invariants*, J. Pure Appl. Algebra**9**(1976/77), no. 2, 195–206. MR**0447268**, https://doi.org/10.1016/0022-4049(77)90066-4**[3]**Melvin Hochster and Joel L. Roberts,*Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay*, Advances in Math.**13**(1974), 115–175. MR**0347810**, https://doi.org/10.1016/0001-8708(74)90067-X**[4]**Tatsuji Kambayashi, Masayoshi Miyanishi, and Mitsuhiro Takeuchi,*Unipotent algebraic groups*, Lecture Notes in Mathematics, Vol. 414, Springer-Verlag, Berlin-New York, 1974. MR**0376696****[5]**Oystein Ore,*On a special class of polynomials*, Trans. Amer. Math. Soc.**35**(1933), no. 3, 559–584. MR**1501703**, https://doi.org/10.1090/S0002-9947-1933-1501703-0**[6]**C. S. Seshadri,*On a theorem of Weitzenböck*, J. Math. Kyoto**1-3**(1962).**[7]**Oscar Zariski and Pierre Samuel,*Commutative algebra. Vol. II*, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR**0120249**

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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