Let k be a field, let be a finite group. We describe linear -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.
@article{bwmeta1.element.doi-10_2478_s11533-008-0002-3, author = {Piotr J\k edrzejewicz}, title = {Linear gradings of polynomial algebras}, journal = {Open Mathematics}, volume = {6}, year = {2008}, pages = {13-24}, zbl = {1137.13001}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0002-3} }
Piotr Jędrzejewicz. Linear gradings of polynomial algebras. Open Mathematics, Tome 6 (2008) pp. 13-24. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-008-0002-3/
[1] Kane R., Reflection groups and invariant theory, Springer-Verlag, New York, Berlin, Heidelberg, 2001 | Zbl 0986.20038
[2] Kraft H., Geometrische Methoden in der Invariantentheorie, Vieweg & Sohn, Braunschweig, 1985 (in German) | Zbl 0669.14003
[3] Li W., Remarks on rings of constants of derivations II, Comm. Algebra, 1992, 20, 2191–2194 http://dx.doi.org/10.1080/00927879208824456 | Zbl 0755.13001
[4] Maubach S., An algorithm to compute the kernel of a derivation up to a certain degree, J. Symbolic Comput., 2000, 29, 959–970 http://dx.doi.org/10.1006/jsco.1999.0334 | Zbl 0999.13011
[5] Nowicki A., Strelcyn J.M., Generators of rings of constants for some diagonal derivations in polynomial rings, J. Pure Appl. Algebra, 1995, 101, 207–212 http://dx.doi.org/10.1016/0022-4049(94)00011-7 | Zbl 0832.12002