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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.

When is a quantum space not a group?

Piotr Mikołaj Sołtan (2010)

Banach Center Publications

We give a survey of techniques from quantum group theory which can be used to show that some quantum spaces (objects of the category dual to the category of C*-algebras) do not admit any quantum group structure. We also provide a number of examples which include some very well known quantum spaces. Our tools include several purely quantum group theoretical results as well as study of existence of characters and traces on C*-algebras describing the considered quantum spaces as well as properties...

Work of Pere Menal on normal subgroups.

Frank A. Arlinghaus, Leonid L. Vaserstein (1992)

Publicacions Matemàtiques

We describe subgroups of GL2A which are normalized by elementary matrices for rings A satisfying the first stable range condition, Banach algebras A, von Neumann regular rings A, and other rings A.

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