Geodesic
RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS
Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 101-111

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be an affine PI-algebra over an algebraically closed field $\mathbb{k}$ and let G be an affine algebraic $\mathbb{k}$-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 centre 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.
DOI : 10.1017/S0017089513000530
Mots-clés : 16R30, 16W22 
LORENZ, MARTIN. RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS. Glasgow mathematical journal, Tome 55 (2013) no. A, pp. 101-111. doi: 10.1017/S0017089513000530
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