Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group
G, is the statement that a map between finite-dimensional kG-modules factors through a …

A ghost over a finite p-group G is a map between modular representations of G which is
invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the …

Freyd's generating hypothesis for the stable module category of a non-trivial finite group $ G
$ is the statement that a map between finitely generated $ kG $-modules that belongs to the …

A theory of ordinal powers of the ideal $\mathfrak {g} _ {\mathcal {S}} $ of $\mathcal {S} $-
ghost morphisms is developed by introducing for every ordinal $\lambda $, the $\lambda …

Let $ G $ be a finite group and let $ k $ be a field of characteristic $ p $. Given a finitely
generated indecomposable nonprojective $ kG $-module $ M $, we conjecture that if the …

Motivated by Freyd's famous unsolved problem in stable homotopy theory, the generating
hypothesis for the stable module category of a finite group is the statement that if a map in …

Let G be a finite group, and let k be a field whose characteristic p divides the order of G.
Freyd's generating hypothesis for the stable module category of G is the statement that a …

We study several closely related invariants of the group algebra k G of a finite group. The
basic invariant is the ghost number, which measures the failure of the generating hypothesis …

We state the generating hypothesis in the homotopy category of G–spectra for a compact Lie
group G and prove that if G is finite, then the generating hypothesis implies the strong …

We introduce Auslander-Reiten sequences for group algebras and give several recent
applications. The first part of the paper is devoted to some fundamental problems in Tate …