Combinatorial triality and representation theory

dc.contributor.advisor J. D. H. Smith Phillips, Jon
dc.contributor.department Mathematics 2018-08-15T04:26:53.000 2020-07-02T06:16:40Z 2020-07-02T06:16:40Z Wed Jan 01 00:00:00 UTC 1992 1992
dc.description.abstract <p>A new subgroup, the endocenter, is defined. The endocenter is a "functorial center". The endocenter also facilitates identification of groups associated with quasigroup modules. We use the endocenter to investigate classes of quasigroups whose combinatorial multiplication group is universal, and classes of quasigroups whose combinatorial multiplication group is not universal;There is a strong connection between groups with triality and Moufang loops. We give a partial classification of those Moufang loops whose combinatorial multiplication group is with triality. We completely characterize all groups with triality associated with cyclic groups. We also identify some universal multiplication groups of Moufang loops and determine their triality status;Unfortunately, the class of groups with triality is not a variety. In an attempt to overcome this apparent deficiency, we axiomatize the variety of "triality groups", and initiate an algebraic investigation of this (and related) varieties;There are strong geometric connections between Moufang loops and groups with triality. We investigate some of these connections;A new class of groups associated with Moufang loops, but more general than the class of groups with triality, is defined. This is the class of groups with biality. We investigate groups with biality and obtain abstract characterizations of multiplication groups of various classes of inverse property loops.</p>
dc.format.mimetype application/pdf
dc.identifier archive/
dc.identifier.articleid 10945
dc.identifier.contextkey 6371712
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/9946
dc.language.iso en
dc.source.bitstream archive/|||Sat Jan 15 02:39:43 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics
dc.title Combinatorial triality and representation theory
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48 dissertation Doctor of Philosophy
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