Fusion systems in group representation theory

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buir.advisorBarker, Laurence J.
dc.contributor.authorTuvay, İpek
dc.date.accessioned2016-01-08T20:03:05Z
dc.date.available2016-01-08T20:03:05Z
dc.date.issued2013
dc.departmentDepartment of Mathematicsen_US
dc.descriptionAnkara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2013.en_US
dc.descriptionThesis (Ph. D.) -- Bilkent University, 2013.en_US
dc.descriptionIncludes bibliographical references leaves 63-65.en_US
dc.description.abstractResults on the Mackey category MF corresponding to a fusion system F and fusion systems defined on p-permutation algebras are our main concern. In the first part, we give a new proof of semisimplicity of MF over C by using a different method than the method used by Boltje and Danz. Following their work in [8], we construct the ghost algebra corresponding to the quiver algebra of MF which is isomorphic to the quiver algebra. We then find a formula for the centrally primitive mutually orthogonal idempotents of this ghost algebra. Then we use this formula to give an alternative proof of semisimplicity of the quiver algebra of MF over the complex numbers. In the second part, we focus on finding classes of p-permutation algebras which give rise to a saturated fusion system which has been studied by Kessar-KunugiMutsihashi in [16]. By specializing to a particular p-permutation algebra and using a result of [16], the question is reduced to finding Brauer indecomposable p-permutation modules. We show for some particular cases of fusion systems we have Brauer indecomposability. In the last part, we study real representations using the real monomial Burnside ring. We deduce a relation on the dimensions of the subgroup-fixed subspaces of a real representation.en_US
dc.description.degreePh.D.en_US
dc.description.statementofresponsibilityTuvay, İpeken_US
dc.format.extentvii, 65 leavesen_US
dc.identifier.urihttp://hdl.handle.net/11693/16916
dc.language.isoEnglishen_US
dc.publisherBilkent Universityen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectfusion systemen_US
dc.subjectMackey categoryen_US
dc.subjectsemisimplicityen_US
dc.subjectp-permutation algebraen_US
dc.subjectBrauer indeomposabilityen_US
dc.subjectmonomial Burnside ringen_US
dc.subject.lccQA176 .T88 2013en_US
dc.subject.lcshGroup theory.en_US
dc.subject.lcshFusion.en_US
dc.subject.lcshBurnside rings.en_US
dc.subject.lcshRings (Algebra).en_US
dc.subject.lcshRepresentations of groups.en_US
dc.titleFusion systems in group representation theoryen_US
dc.typeThesisen_US

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