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

Title:

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

Creator:

Zeng, Lingli and Nan, Jizhu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:b119d902-9223-4684-9168-cfb09ff69edf
uuid:b119d902-9223-4684-9168-cfb09ff69edf
issn:0011-4642

Subject:

matematika, vektorová algebra, mathematics, vector algebra, vector invariant ideal, group algebra, unitary group, orthogonal group, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let F be a finite field of characteristic p and K a field which contains a primitive pth root of unity and char K ≠ p. Suppose that a classical group G acts on the F-vector space V. Then it can induce the actions on the vector space \left [ V\bigoplus V \right ] and on the group algebra K\left [ V\bigoplus V \right ], respectively. In this paper we determine the structure of G-invariant ideals of the group algebra K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], and establish the relationship between the invariant ideals of K[V] and the vector invariant ideals of K\left [ V\bigoplus V \right ], 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., Lingli Zeng, Jizhu Nan., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

1059-1078

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:4

Harvested from:

CDK

Metadata only:

false