Terwilliger algebras of wreath products of association schemes

dc.contributor.advisor Sung Yell Song
dc.contributor.advisor Leslie Hogben
dc.contributor.advisor Elgin Johnston
dc.contributor.author Bhattacharyya, Gargi
dc.contributor.department Mathematics
dc.date 2018-08-22T18:06:58.000
dc.date.accessioned 2020-06-30T07:46:23Z
dc.date.available 2020-06-30T07:46:23Z
dc.date.copyright Tue Jan 01 00:00:00 UTC 2008
dc.date.issued 2008-01-01
dc.description.abstract <p>In this thesis, we study the T -algebras of symmetric association schemes that are obtained as the wreath product of H(1, m) for m ≥ 2. We find that the D-class association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD formed by taking the wreath product of one-class association schemes Kni = H(1, ni) has the triple-regularity property. We determine the dimension of the T -algebra for the association scheme Kn1&m22;Kn2&m22;&cdots; &m22;KnD . We also show that the wreath power Km&m22;D =Km&m22;Km&m22;&cdots;&m22;Km , D copies of Km, is formally self-dual. We give a complete description of the irreducible T -modules and the structure of T -algebra for Km&m22;D for m ≥ 2 by essentially studying the irreducible modules of 2 copies of Km and then extending it to the general case for D copies of Km. Through these calculations we obtain that the T -algebra for Km&m22;D is MD+1C ⊕C⊕12 DD+1 for m ≥ 3, and MD+1C ⊕C⊕12 DD-1 m = 2.</p>
dc.format.mimetype application/pdf
dc.identifier archive/lib.dr.iastate.edu/rtd/15679/
dc.identifier.articleid 16678
dc.identifier.contextkey 7040805
dc.identifier.doi https://doi.org/10.31274/rtd-180813-16891
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath rtd/15679
dc.identifier.uri https://dr.lib.iastate.edu/handle/20.500.12876/69334
dc.language.iso en
dc.source.bitstream archive/lib.dr.iastate.edu/rtd/15679/3316196.PDF|||Fri Jan 14 20:44:45 UTC 2022
dc.subject.disciplines Mathematics
dc.subject.keywords Mathematics;
dc.title Terwilliger algebras of wreath products of association schemes
dc.type article
dc.type.genre dissertation
dspace.entity.type Publication
relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
thesis.degree.level dissertation
thesis.degree.name Doctor of Philosophy
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