Miki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebra

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dc.contributor.authorQuinlan, Isis Angelina Marieen
dc.contributor.committeechairOrr, Daniel D.en
dc.contributor.committeememberShimozono, Mark M.en
dc.contributor.committeememberMatthews, Gretchen L.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2020-06-05T08:01:08Zen
dc.date.available2020-06-05T08:01:08Zen
dc.date.issued2020-06-04en
dc.description.abstractThrough composition of isomorphisms from results by Miki and Negut, this paper seeks to simplify calculations of the images of generators of the quantum toroidal algebra. We will be working in the small shuffle algebra, which is isomorphic to the positive part of the quantum toroidal algebra. There, we will be computing commutators, which are equal to images under the Miki automorphism, though are much simpler to compute.en
dc.description.abstractgeneralComputing is hard, even for computers. The fewer computations we have to do, the more time we can save to do more math. This paper accomplishes just that. By looking at the quantum toroidal algebra through an automorphism followed by an isomorphism to a small shuffle algebra, we find a way to compute images of generators under the automorphism relatively easily.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:26119en
dc.identifier.urihttp://hdl.handle.net/10919/98753en
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectAlgebraen
dc.titleMiki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebraen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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