Difference between revisions of "Open problems"
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== General problems == | == General problems == | ||
| − | * Is the isomorphism type of the defect group a Morita invariant? | + | * [[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? | ||
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* 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). | * 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). | ||
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== Basic algebras of dimension 9 == | == 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? | 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? | ||
Revision as of 13:53, 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?
