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

Lingli Zeng, Jizhu Nan (2016)

Czechoslovak Mathematical Journal

Let F be a finite field of characteristic p and K a field which contains a primitive p th 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 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....

Veränderungen über einen Satz von Timmesfeld – I. Quadratic Actions

Adrien Deloro (2013)

Confluentes Mathematici

We classify quadratic SL 2 ( 𝕂 ) - and 𝔰𝔩 2 ( 𝕂 ) -modules by crude computation, generalising in the first case a Theorem proved independently by F.G. Timmesfeld and S. Smith. The paper is the first of a series dealing with linearisation results for abstract modules of algebraic groups and associated Lie rings.

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