Linear gradings of polynomial algebras

Piotr Jędrzejewicz

Open Mathematics (2008)

  • Volume: 6, Issue: 1, page 13-24
  • ISSN: 2391-5455

Abstract

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Let k be a field, let G be a finite group. We describe linear G -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.

How to cite

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Piotr Jędrzejewicz. "Linear gradings of polynomial algebras." Open Mathematics 6.1 (2008): 13-24. <http://eudml.org/doc/269198>.

@article{PiotrJędrzejewicz2008,
abstract = {Let k be a field, let \[ G \] be a finite group. We describe linear \[ G \] -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.},
author = {Piotr Jędrzejewicz},
journal = {Open Mathematics},
keywords = {graded algebra; polynomial algebra},
language = {eng},
number = {1},
pages = {13-24},
title = {Linear gradings of polynomial algebras},
url = {http://eudml.org/doc/269198},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Piotr Jędrzejewicz
TI - Linear gradings of polynomial algebras
JO - Open Mathematics
PY - 2008
VL - 6
IS - 1
SP - 13
EP - 24
AB - Let k be a field, let \[ G \] be a finite group. We describe linear \[ G \] -gradings of the polynomial algebra k[x 1, ..., x m] such that the unit component is a polynomial k-algebra.
LA - eng
KW - graded algebra; polynomial algebra
UR - http://eudml.org/doc/269198
ER -

References

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  1. [1] Kane R., Reflection groups and invariant theory, Springer-Verlag, New York, Berlin, Heidelberg, 2001 Zbl0986.20038
  2. [2] Kraft H., Geometrische Methoden in der Invariantentheorie, Vieweg & Sohn, Braunschweig, 1985 (in German) Zbl0669.14003
  3. [3] Li W., Remarks on rings of constants of derivations II, Comm. Algebra, 1992, 20, 2191–2194 http://dx.doi.org/10.1080/00927879208824456 Zbl0755.13001
  4. [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 Zbl0999.13011
  5. [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 Zbl0832.12002

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