Generalizations of Cayley's -process |
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Authors: | Walter Ferrer Santos Alvaro Rittatore |
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Institution: | Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay ; Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay |
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Abstract: | In this paper we axiomatize some constructions and results due to Cayley and Hilbert. We define the concept of -process for an arbitrary affine algebraic monoid with zero and unit group . In our situation we show how to produce from the process and for a linear rational representation of a number of elements of the ring of -invariants that is large enough to guarantee its finite generation. Moreover, using complete reducibility, we give an explicit construction of all -processes for reductive monoids. |
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