CompletedGroupAlgebra.Augmentation

4 sections | 4 files | 30 declarations

This module develops completed group algebras through finite quotient stages, transition maps, coefficient change, augmentation, comparison maps, and inverse-limit topology.

AugmentationIdeal

1 files | 6 declarations | 5 Theorem | 1 Definition

The canonical augmentation ideal of the \(C\)-indexed completed group algebra.

CanonicalAugmentation

1 files | 12 declarations | 10 Theorem | 2 Definition

The \(C\)-indexed completed augmentation evaluated at a finite stage.

Functoriality

1 files | 5 declarations | 5 Theorem

The in-class canonical augmentation is natural under functorial completed maps.

StageAugmentation

1 files | 7 declarations | 6 Theorem | 1 Definition

The augmentation map on one \(C\)-indexed finite stage.