ProCGroups.CompletedGroupAlgebra.ProfiniteModules.FiniteGroupAlgebra

4 sections | 6 files | 96 declarations

This aggregate exports the profinite topology and universal lifting maps for finite group algebras, their augmentation theory, functoriality in the group, and group-like unit representations on modules.

imports

Imported by

ProCGroups.CompletedGroupAlgebra.ProfiniteModules

Augmentation

3 files | 47 declarations | 35 Theorems | 12 Definitions

This file defines augmentation of an abstract group algebra, its linear form and kernel ideal, and the resulting short exact sequences. It also proves that the differences \(g-1...

Functoriality

1 file | 23 declarations | 21 Theorems | 2 Definitions

This file studies group-algebra maps induced by homomorphisms of finite groups, including composition, basis formulas, continuity, and surjectivity. It also develops coefficient...

Topology

1 file | 15 declarations | 11 Theorems | 4 Definitions

A finite group algebra over a profinite coefficient ring is identified with a finite product of coefficients and given its profinite ring topology. This file proves continuity o...

UnitRepresentation

1 file | 11 declarations | 8 Theorems | 3 Definitions

Groups embed as units in their algebraic and completed group algebras. This file relates that representation to augmentation and shows how restriction of scalars gives continuou...