{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/98753"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/98753","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Miki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebra","abstract":"Through 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.","abstract_html":"Through 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.","abstract_has_math":false,"creators":["Quinlan, Isis Angelina Marie"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Orr, Daniel D."],"committee_members":["Shimozono, Mark M.","Matthews, Gretchen L."],"year":2020,"date_issued":"2020-06-04","date_published":"2020-06-04","updated_at":"2026-07-22T22:20:02Z","subjects":["Algebra"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:26119"],"render_values":[{"text":"vt_gsexam:26119","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/98753","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Orr, Daniel D."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Shimozono, Mark M.","Matthews, Gretchen L."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Quinlan, Isis Angelina Marie"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2020-06-05T08:01:08Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2020-06-05T08:01:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2020-06-04"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Algebra"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["vt_gsexam:26119"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/98753"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Through 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."]},{"key":"dc:description.abstractgeneral","label":"General Abstract","values":["Computing 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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["ETD"]},{"key":"dc:title","label":"Title","values":["Miki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebra"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Orr, Daniel D."],"dc:contributor.committeemember":["Shimozono, Mark M.","Matthews, Gretchen L."],"dc:contributor.department":["Mathematics"],"dc:creator":["Quinlan, Isis Angelina Marie"],"dc:date.accessioned":["2020-06-05T08:01:08Z"],"dc:date.available":["2020-06-05T08:01:08Z"],"dc:date.issued":["2020-06-04"],"dc:description.abstract":["Through 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."],"dc:description.abstractgeneral":["Computing 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."],"dc:description.degree":["Master of Science"],"dc:format.medium":["ETD"],"dc:identifier.other":["vt_gsexam:26119"],"dc:identifier.uri":["http://hdl.handle.net/10919/98753"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Algebra"],"dc:title":["Miki Images of Quantum Toroidal Algebra Generators in the Shuffle Algebra"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:02Z"}