Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [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 $ {G_a}$-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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14L99

Retrieve articles in all journals with MSC: 14L99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1977-0460345-3
Keywords: $ {G_a}$-actions, ring of invariants
Article copyright: © Copyright 1977 American Mathematical Society

American Mathematical Society