Persistent Link:
http://hdl.handle.net/10150/194298
Title:
Computing the Cohomology Ring and Ext-Algebra of Group Algebras
Author:
Pawloski, Robert Michael
Issue Date:
2006
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 and its implementation in the computer algebra system GAP for constructing the cohomology ring and Ext-algebra for certain group algebras kG. We compute in the Morita equivalent basic algebra B of kG and obtain the cohomology ring and Ext-algebra for the group algebra kG up to isomorphism. As this work is from a computational point of view, we consider the cohomology ring and Ext-algebra via projective resolutions.There are two main methods for computing projective resolutions. One method uses linear algebra and the other method uses noncommutative Grobner basis theory. Both methods are implemented in GAP and results in terms of timings are given. To use the noncommutative Grobner basis theory, we have implemented and designed an alternative algorithm to the Buchberger algorithm when given a finite dimensional algebra in terms of a basis consisting of monomials in the generators of the algebra and action of generators on the basis.The group algebras we are mainly concerned with here are for simple groups in characteristic dividing the order of the group. We have computed the Ext-algebra and cohomology ring for a variety of simple groups to a given degree and have thus added many more examples to the few that have thus far been computed.
Type:
text; Electronic Dissertation
Keywords:
Group; cohomology; Ext; group algebra
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Lux, Klaus
Committee Chair:
Lux, Klaus

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleComputing the Cohomology Ring and Ext-Algebra of Group Algebrasen_US
dc.creatorPawloski, Robert Michaelen_US
dc.contributor.authorPawloski, Robert Michaelen_US
dc.date.issued2006en_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 and its implementation in the computer algebra system GAP for constructing the cohomology ring and Ext-algebra for certain group algebras kG. We compute in the Morita equivalent basic algebra B of kG and obtain the cohomology ring and Ext-algebra for the group algebra kG up to isomorphism. As this work is from a computational point of view, we consider the cohomology ring and Ext-algebra via projective resolutions.There are two main methods for computing projective resolutions. One method uses linear algebra and the other method uses noncommutative Grobner basis theory. Both methods are implemented in GAP and results in terms of timings are given. To use the noncommutative Grobner basis theory, we have implemented and designed an alternative algorithm to the Buchberger algorithm when given a finite dimensional algebra in terms of a basis consisting of monomials in the generators of the algebra and action of generators on the basis.The group algebras we are mainly concerned with here are for simple groups in characteristic dividing the order of the group. We have computed the Ext-algebra and cohomology ring for a variety of simple groups to a given degree and have thus added many more examples to the few that have thus far been computed.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectGroupen_US
dc.subjectcohomologyen_US
dc.subjectExten_US
dc.subjectgroup algebraen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorLux, Klausen_US
dc.contributor.chairLux, Klausen_US
dc.contributor.committeememberJoshi, Kirtien_US
dc.contributor.committeememberGrove, Larryen_US
dc.contributor.committeememberMcCallum, Williamen_US
dc.contributor.committeememberUlmer, Dougen_US
dc.identifier.proquest1492en_US
dc.identifier.oclc659746262en_US
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