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Czechoslovak Mathematical Journal

, Volume 66, Issue 4, pp 1059–1078 | Cite as

Vector invariant ideals of abelian group algebras under the actions of the unitary groups and orthogonal groups

  • Lingli Zeng
  • Jizhu Nan
Article
  • 52 Downloads

Abstract

Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char Kp. Suppose that a classical group G acts on the F-vector space V. Then it can induce the actions on the vector space V
V and on the group algebra K[V
V], respectively. In this paper we determine the structure of G-invariant ideals of the group algebra K[V
V], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K[V
V], if G is a unitary group or orthogonal group. Combining the results obtained by Nan and Zeng (2013), we solve the problem of vector invariant ideals for all classical groups over finite fields.

Keywords

vector invariant ideal group algebra unitary group orthogonal group 

MSC 2010

16S34 20G40 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2016

Authors and Affiliations

  1. 1.Department of MathematicsNorthwest UniversityShaanxiP.R. China
  2. 2.School of Mathematical SciencesDalian University of TechnologyDalian Ganjingzi, LiaoningP.R. China

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