Difference between revisions of "Glossary"
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The classification of finite simple groups. | The classification of finite simple groups. | ||
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| + | === Fusion system === | ||
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| + | Fusion system on a finite <math>p</math>-group. See [[References|[Cr11] or [AKO11]]]. The fusion system given by a finite group <math>G</math> on a Sylow <math>p</math>-subgroup <math>P</math> is written <math>\mathcal{F}_P(G)</math>. | ||
=== # lifts / <math>\mathcal{O}</math> === | === # lifts / <math>\mathcal{O}</math> === | ||
Revision as of 07:30, 5 October 2018
This page will contain an alphabetical glossary of terms used.
Contents
Basic Morita/stable equivalence
Morita/stable equivalence of blocks induced by a bimodule which has endopermutation source.
CFSG
The classification of finite simple groups.
Fusion system
Fusion system on a finite [math]p[/math]-group. See [Cr11] or [AKO11]. The fusion system given by a finite group [math]G[/math] on a Sylow [math]p[/math]-subgroup [math]P[/math] is written [math]\mathcal{F}_P(G)[/math].
# 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].
