Generalizations of Cayley’s $\Omega$-process
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- by Walter Ferrer Santos and Alvaro Rittatore PDF
- Proc. Amer. Math. Soc. 135 (2007), 961-968 Request permission
Abstract:
In this paper we axiomatize some constructions and results due to Cayley and Hilbert. We define the concept of $\Omega$–process for an arbitrary affine algebraic monoid with zero and unit group $G$. In our situation we show how to produce from the process and for a linear rational representation of $G$ a number of elements of the ring of $G$-invariants $S(V)^G$ that is large enough to guarantee its finite generation. Moreover, using complete reducibility, we give an explicit construction of all $\Omega$-processes for reductive monoids.References
- Walter Ferrer Santos and Alvaro Rittatore, Actions and invariants of algebraic groups, Pure and Applied Mathematics (Boca Raton), vol. 269, Chapman & Hall/CRC, Boca Raton, FL, 2005. MR 2138858, DOI 10.1201/9781420030792
- David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, DOI 10.1007/BF01208503
- Mohan S. Putcha, Linear algebraic monoids, London Mathematical Society Lecture Note Series, vol. 133, Cambridge University Press, Cambridge, 1988. MR 964690, DOI 10.1017/CBO9780511600661
- Lex E. Renner, Linear algebraic monoids, Encyclopaedia of Mathematical Sciences, vol. 134, Springer-Verlag, Berlin, 2005. Invariant Theory and Algebraic Transformation Groups, V. MR 2134980
- A. Rittatore, Algebraic monoids and group embeddings, Transform. Groups 3 (1998), no. 4, 375–396. MR 1657536, DOI 10.1007/BF01234534
- Bernd Sturmfels, Algorithms in invariant theory, Texts and Monographs in Symbolic Computation, Springer-Verlag, Vienna, 1993. MR 1255980, DOI 10.1007/978-3-7091-4368-1
Additional Information
- Walter Ferrer Santos
- Affiliation: Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
- Email: wrferrer@cmat.edu.uy
- Alvaro Rittatore
- Affiliation: Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
- Email: alvaro@cmat.edu.uy
- Received by editor(s): August 30, 2005
- Received by editor(s) in revised form: October 31, 2005
- Published electronically: September 26, 2006
- Additional Notes: The first author would like to thank Csic-UDELAR and Conicyt-MEC
The second author would like to thank FCE-MEC, project number 10018 - Communicated by: Martin Lorenz
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 961-968
- MSC (2000): Primary 20G20, 16W22, 14Lxx
- DOI: https://doi.org/10.1090/S0002-9939-06-08546-7
- MathSciNet review: 2262895