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

DOI

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
@article{10_1017_S0017089513000530,
     author = {LORENZ, MARTIN},
     title = {RATIONAL {GROUP} {ACTIONS} {ON} {AFFINE} {PI-ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {101--111},
     year = {2013},
     volume = {55},
     number = {A},
     doi = {10.1017/S0017089513000530},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000530/}
}
TY  - JOUR
AU  - LORENZ, MARTIN
TI  - RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS
JO  - Glasgow mathematical journal
PY  - 2013
SP  - 101
EP  - 111
VL  - 55
IS  - A
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000530/
DO  - 10.1017/S0017089513000530
ID  - 10_1017_S0017089513000530
ER  - 
%0 Journal Article
%A LORENZ, MARTIN
%T RATIONAL GROUP ACTIONS ON AFFINE PI-ALGEBRAS
%J Glasgow mathematical journal
%D 2013
%P 101-111
%V 55
%N A
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089513000530/
%R 10.1017/S0017089513000530
%F 10_1017_S0017089513000530

Cité par Sources :