# Difference between revisions of "Open problems"

Line 3: | Line 3: | ||

== General problems == | == General problems == | ||

− | * [[Is the isomorphism type of the defect group a Morita invariant?]] | + | * [[Morita invariance of the isomorphism type of a defect group|Is the isomorphism type of the defect group a Morita invariant?]] |

* Is <math>{\rm Pic}_\mathcal{O}(B)</math> always finite? | * Is <math>{\rm Pic}_\mathcal{O}(B)</math> always finite? | ||

* Is every Morita equivalence between <math>\mathcal{O}</math>-blocks endopermutation source? | * Is every Morita equivalence between <math>\mathcal{O}</math>-blocks endopermutation source? |

## Revision as of 15:47, 3 January 2019

This page is for open problems, large and small, relating to module categories for blocks. Missing data is also flagged within tables elsewhere on this site.

## General problems

- Is the isomorphism type of the defect group a Morita invariant?
- Is [math]{\rm Pic}_\mathcal{O}(B)[/math] always finite?
- Is every Morita equivalence between [math]\mathcal{O}[/math]-blocks endopermutation source?

## Open cases for classifications of Morita equivalence classes for a given [math]p[/math]-group

- Which Brauer trees give rise to blocks with defect group [math]C_7[/math]? (This is the smallest cyclic group for which the classification is not known).

## Basic algebras of dimension 9

Does the 9-dimensional algebra described in Blocks with basic algebras of low dimension occur as the basic algebra of a block of a finite group?