Constructing basic algebras for the principal block of sporadic simple groups

Persistent Link:
http://hdl.handle.net/10150/280550
Title:
Constructing basic algebras for the principal block of sporadic simple groups
Author:
Hoffman, Thomas Rune
Issue Date:
2004
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
This dissertation describes an algorithm for constructing the basic algebra Morita equivalent to the principal block of certain group algebras. This algorithm uses the method of condensation as it is described in [Lux97]. Using an intermediate condensation subalgebra allows for the construction of the projective indecomposable modules required to realize the basic algebra. The group algebras we are concerned with here are for sporadic groups in characteristic dividing the order of the group. In particular, the basic algebra for the principal block of the Higman-Sims group in characteristic 2 is completed and seven of the thirteen projective indecomposable modules for the Mathieu group M24 are constructed. In addition to these algebras, we have also computed the basic algebras for many alternating and symmetric groups.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Mathematics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Mathematics
Degree Grantor:
University of Arizona
Advisor:
Lux, Klaus

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleConstructing basic algebras for the principal block of sporadic simple groupsen_US
dc.creatorHoffman, Thomas Runeen_US
dc.contributor.authorHoffman, Thomas Runeen_US
dc.date.issued2004en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThis dissertation describes an algorithm for constructing the basic algebra Morita equivalent to the principal block of certain group algebras. This algorithm uses the method of condensation as it is described in [Lux97]. Using an intermediate condensation subalgebra allows for the construction of the projective indecomposable modules required to realize the basic algebra. The group algebras we are concerned with here are for sporadic groups in characteristic dividing the order of the group. In particular, the basic algebra for the principal block of the Higman-Sims group in characteristic 2 is completed and seven of the thirteen projective indecomposable modules for the Mathieu group M24 are constructed. In addition to these algebras, we have also computed the basic algebras for many alternating and symmetric groups.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMathematics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLux, Klausen_US
dc.identifier.proquest3132228en_US
dc.identifier.bibrecord.b46708789en_US
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