CompletedGroupAlgebra.ProfiniteModules.FiniteGroupAlgebra

4 sections | 6 files | 100 declarations

The completed group algebra is presented as an inverse limit of finite group algebras, together with canonical augmentation, augmentation ideal, finite-stage maps, functoriality, and profinite module universal properties.

Augmentation

3 files | 47 declarations | 35 Theorem | 12 Definition

Wrapper for the `CompletedGroupAlgebra.ProfiniteModules.FiniteGroupAlgebra.Augmentation` folder.

Functoriality

1 files | 24 declarations | 22 Theorem | 2 Definition

Finite-stage group algebras are functorial by continuous ring homomorphisms.

Topology

1 files | 18 declarations | 12 Theorem | 5 Definition | 1 Structure

A completed-group-algebra model consists of a profinite coefficient ring, a profinite group, a profinite topological ring carrier, and a dense algebraic group-algebra map from a...

UnitRepresentation

1 files | 11 declarations | 8 Theorem | 3 Definition

The canonical embedding of a group into the units of its abstract group algebra.