Difference between revisions of "Open problems"
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== Picard groups == | == Picard groups == | ||
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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 15:26, 4 October 2018
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.
Contents
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).
Picard groups
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?
