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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Generalizations of Cayley's $ \Omega$-process


Authors: Walter Ferrer Santos and Alvaro Rittatore
Journal: Proc. Amer. Math. Soc. 135 (2007), 961-968
MSC (2000): Primary 20G20, 16W22, 14Lxx
Published electronically: September 26, 2006
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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.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08546-7
PII: S 0002-9939(06)08546-7
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
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.