On the depth of separating invariants for finite groups

Article


Elmer, J. 2012. On the depth of separating invariants for finite groups. Beitrage zur Algebra und Geometrie. 53 (1), pp. 31-39.
TypeArticle
TitleOn the depth of separating invariants for finite groups
AuthorsElmer, J.
Abstract

Abstract. Consider a finite group G acting on a vector space V
over a field k of characteristic p > 0. A separating algebra is a
subalgebra A of the ring of invariants k[V]^G with the same point
separation properties. In this article we compare the depth of an
arbitrary separating algebra with that of the corresponding ring of
invariants. We show that, in some special cases, the depth of A is
bounded above by the depth of k[V]^G .

LanguageEnglish
PublisherSpringer Verlag
JournalBeitrage zur Algebra und Geometrie
ISSN0138-4821
Publication dates
PrintMar 2012
Publication process dates
Deposited15 Apr 2016
Accepted10 May 2011
Output statusPublished
Accepted author manuscript
Web address (URL)http://link.springer.com/article/10.1007%2Fs13366-011-0030-1
Permalink -

https://repository.mdx.ac.uk/item/863xy

Download files


Accepted author manuscript
  • 22
    total views
  • 2
    total downloads
  • 0
    views this month
  • 0
    downloads this month

Export as

Related outputs

The separating variety for 2 x 2 matrix invariants
Elmer, J. 2024. The separating variety for 2 x 2 matrix invariants. Linear and Multilinear Algebra. 72 (3), pp. 389-411. https://doi.org/10.1080/03081087.2022.2158300
The separating variety for matrix semi-invariants
Elmer, J. 2023. The separating variety for matrix semi-invariants. Linear Algebra and its Applications. 674, pp. 466-492. https://doi.org/10.1016/j.laa.2023.06.012
Modular covariants of cyclic groups of order p
Elmer, J. 2022. Modular covariants of cyclic groups of order p. Journal of Algebra. 598, pp. 134-155. https://doi.org/10.1016/j.jalgebra.2022.01.015
The relative Heller operator and relative cohomology for the Klein 4-group
Elmer, J. 2022. The relative Heller operator and relative cohomology for the Klein 4-group. Communications in Algebra. 50 (4), pp. 1518-1534. https://doi.org/10.1080/00927872.2021.1984496
Degree bounds for modular covariants
Elmer, J. and Sezer, M. 2020. Degree bounds for modular covariants. Forum Mathematicum. 32 (4), pp. 905-910. https://doi.org/10.1515/forum-2019-0196
Locally finite derivations and modular coinvariants
Elmer, J. and Sezer, M. 2018. Locally finite derivations and modular coinvariants. Quarterly Journal of Mathematics. 69 (3), pp. 1053-1062. https://doi.org/10.1093/qmath/hay013
Symmetric powers and modular invariants of elementary abelian p-groups
Elmer, J. 2017. Symmetric powers and modular invariants of elementary abelian p-groups. Journal of Algebra. 492, pp. 157-184. https://doi.org/10.1016/j.jalgebra.2017.07.020
On separating a fixed point from zero by invariants
Elmer, J. and Kohls, M. 2017. On separating a fixed point from zero by invariants. Communications in Algebra. 45 (1), pp. 371-375. https://doi.org/10.1080/00927872.2016.1175465
Zero-separating invariants for linear algebraic groups
Elmer, J. and Kohls, M. 2016. Zero-separating invariants for linear algebraic groups. Proceedings of the Edinburgh Mathematical Society. 59 (4), pp. 911-924. https://doi.org/10.1017/S0013091515000322
Zero-separating invariants for finite groups
Elmer, J. and Kohls, M. 2014. Zero-separating invariants for finite groups. Journal of Algebra. 411, pp. 92-113. https://doi.org/10.1016/j.jalgebra.2014.03.044
Separating invariants for arbitrary linear actions of the additive group
Dufresne, E., Elmer, J. and Sezer, M. 2014. Separating invariants for arbitrary linear actions of the additive group. Manuscripta Mathematica. 143 (1), pp. 207-219. https://doi.org/10.1007/s00229-013-0625-y
Separating Invariants for the Basic G_a actions
Elmer, J. and Kohls, M. 2012. Separating Invariants for the Basic G_a actions. Proceedings of the American Mathematical Society. 140 (1), pp. 135-146.
The Cohen-Macaulay property of separating invariants of finite groups
Dufresne, E., Elmer, J. and Kohls, M. 2009. The Cohen-Macaulay property of separating invariants of finite groups. Transformation Groups. 14 (4), pp. 771-785.
Depth and detection in modular invariant theory
Elmer, J. 2009. Depth and detection in modular invariant theory. Journal of Algebra. 322 (5), pp. 1653-1666. https://doi.org/10.1016/j.jalgebra.2009.04.036
On the depth of modular invariant rings for the groups C_p x C_p
Elmer, J. and Fleischmann, P. 2009. On the depth of modular invariant rings for the groups C_p x C_p. in: Symmetry and Spaces: in honour of Gerry Schwarz Birkhauser Boston.
Associated primes for cohomology modules
Elmer, J. 2008. Associated primes for cohomology modules. Archiv der Mathematik. 91 (6), pp. 481-485. https://doi.org/10.1007/s00013-008-2902-7