Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

A new degree bound for invariant rings

Author(s): Jianjun Chuai
Journal: Proc. Amer. Math. Soc. 133 (2005), 1325-1333.
MSC (2000): Primary 13A50
Posted: November 19, 2004
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

Abstract: In this paper we give a new degree bound for polynomial invariant rings of finite groups and give some applications.


References:

1.
A. Broer, Remarks on invariant theory of finite groups, Preprint, Université de Montréal, Montréal, (1997).

2.
H. E. A. Campbell, A. V. Geramita, I. P. Hughes, R. J. Shank and D. L. Wehlau, Non-Cohen-Macaulay vector invariants and a Noether bound for a Gorenstein ring of invariants, Canad. Math. Bull. 42(2)(1999), 155-161. MR 1692004 (2000b:13005)

3.
H. E. A. Campbell and I. P. Hughes, Vector invariants of $U_2(\mathbf{F}_p)$: A proof of a conjecture of Richman, Adv. in Math. 126(1997), 1-20. MR 1440251 (98c:13007)

4.
Jianjun Chuai, Two-dimensional vector invariant rings of Abelian $p$-groups, J. of Alg. 266(1)(2003), 362-373. MR 1994545 (2004e:13010)

5.
H. Derksen and G. Kemper, Computational invariant theory, Springer, (2002). MR 1918599 (2003g:13004)

6.
J. A. Eagon and M. Hochster, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93(1971), 1020-1058. MR 0302643 (46:1787)

7.
P. Fleischmann, On invariants theory of finite groups, Preprint, Invariant Theory Workshop at Queen's University, (2002).

8.
P. Fleischmann, The Noether bound in invariant theory of finite groups, Adv. in Math. 156(2000), 23-32. MR 1800251 (2001k:13009)

9.
J. Fogarty, On Noether's bound for polynomial invariants of a finite group, Elec. Res. Announ. of the Amer. Math. Soc. 7(2001), 5-7. MR 1826990 (2002a:13002)

10.
M. Goebel, Computing bases for rings of permutation-invariant polynomials, J. Symb. Comp., 19 (1995), 285-291. MR 1339909 (96f:13006)

11.
I. Hughes and G. Kemper, Symmetric powers of modular representations, Hilbert series and degree bounds, Comm. Alg., 28(4) (2000), 2059-2088. MR 1747371 (2001b:13009)

12.
D. B. Karagueuzian and Peter Symonds, The module structure of a group action on a polynomial ring: the general case, Preprint, (2001).

13.
E. Noether, Der Endlichkeitssatz der Invarianten endlicher Gruppen, Math. Ann. 77(1916), 89-92.

14.
D. R. Richman, On vector invariants over finite fields, Adv. in Math. 81(1990), 30-65. MR 1051222 (91g:15020)

15.
L. Smith, Polynomial invariants of finite groups, A. K. Peter, Ltd. 1995. MR 1328644 (96f:13008)

16.
R. P. Stanley, Polynomial invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. 1(3) (1979), 475-511. MR 0526968 (81a:20015)

17.
H. Weyl, The classical groups, Princeton University Press, Princeton, NJ, (1939). MR 0000255 (1:42c)


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 13A50

Retrieve articles in all Journals with MSC (2000): 13A50


Additional Information:

Jianjun Chuai
Affiliation: Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada K7L 3N6
Email: chuai@mast.queensu.ca

DOI: 10.1090/S0002-9939-04-07787-1
PII: S 0002-9939(04)07787-1
Keywords: Invariant ring, degree bound
Received by editor(s): September 23, 2003
Received by editor(s) in revised form: January 30, 2004
Posted: November 19, 2004
Additional Notes: This research was partially supported by NSERC
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2004, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google