Generalized Cayley's $Ω$-processes

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In this paper we generalize some constructions and results due to Cayley and Hilbert. We define the concept of $Ω$--process for an arbitrary algebraic monoid with zero and unit group $G$. Then 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, that is large enough as to guarantee its finite generation. Moreover, we give an explicit construction of all $Ω$-processes for general reductive monoids and, in the case of the monoid of all the $n^2$ matrices, compare our construction with Cayley's definition.
17 pages

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Algebraic Geometry, Representation Theory, 20G05;16W22;14L35

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http://salesiana.dossiersoluciones.com/handle/123456789/76125

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0508436
 http://arxiv.org/abs/math/0508436

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arXiv