Extensions of Enveloping Algebras Via Anti-cocommutative Elements

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dc.contributor.advisorAllen D. Bell
dc.contributor.committeememberAllen D. Bell
dc.contributor.committeememberCraig R. Guilbault
dc.contributor.committeememberIan M. Musson
dc.contributor.committeememberJeb F. Willenbring
dc.contributor.committeememberYi M. Zou
dc.creatorYee, Daniel Owen
dc.date.accessioned2025-01-16T18:07:13Z
dc.date.available2025-01-16T18:07:13Z
dc.date.issued2017-08-01
dc.description.abstractWe know that given a connected Hopf algebra H, the universal enveloping algebra U(P(H)) embeds in H as a Hopf subalgebra. Depending on P(H), we show that there may be another enveloping algebra (not as a Hopf subalgebra) within H by using anti-cocommutative elements. Thus, this is an extension of enveloping algebras with regards to the Hopf structure. We also use these discoveries to apply to global dimension, and finish with antipode behavior and future research projects.
dc.identifier.urihttp://digital.library.wisc.edu/1793/86079
dc.relation.replaceshttps://dc.uwm.edu/etd/1728
dc.subjectAnti-cocommutative
dc.subjectConnected Algebra
dc.subjectEnveloping Algebra
dc.subjectGlobal Dimension
dc.subjectHOPF Algebra
dc.subjectNon-commutative Algebra
dc.titleExtensions of Enveloping Algebras Via Anti-cocommutative Elements
dc.typedissertation
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Wisconsin-Milwaukee
thesis.degree.nameDoctor of Philosophy

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