Glossary

This page will contain an alphabetical glossary of terms used.

# lifts / [math]\mathcal{O}[/math]

The number of [math]\mathcal{O}[/math]-Morita equivalence classes of blocks reducing to a representative of the given [math]k[/math]-class.

Picard group

Let [math]R[/math] be a commutative ring and [math]A[/math] an [math]R[/math]-algebra. The Picard group [math]{\rm Pic}_R(A)[/math] has elements isomorphism classes of [math]A[/math]-[math]A[/math]-bimodules inducing a Morita equivalence, with multiplication given by taking tensor products over [math]A[/math].

Possible Brauer tree (for a given cyclic defect group)

Given a cyclic [math]p[/math]-group [math]P[/math], the Brauer trees whose vertex multiplicities add to [math]|P|[/math], where non-exceptional vertices are regarded as having multiplicity [math]1[/math].