Rational group actions on affine PI-algebras

Details Rational group actions on affine PI-algebras Rational group actions on affine PI-algebras

2011-05-20

arxiv.org/abs/1105.4121v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

Let R be an affine PI-algebra over an algebraically closed field k and let G be an affine algebraic k-group that acts rationally by algebra automorphisms on R. For R prime and G a torus, we show that R has only finitely many G-prime ideals if and only if the action of G on the center of R is multiplicity free. This extends a standard result on affine algebraic G-varieties. Under suitable hypotheses on R and G, we also prove a PI-version of a well-known result on spherical varieties and a version of Schelter's catenarity theorem for G-primes.

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