Difference between revisions of "Glossary"
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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>. | 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>. | ||
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| + | === Possible Brauer tree (for a given cyclic defect group) === | ||
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| + | 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>. | ||
Revision as of 09:30, 15 September 2018
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].
