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. / Master of Science / 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.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/98753 |
| Date | 04 June 2020 |
| Creators | Quinlan, Isis Angelina Marie |
| Contributors | Mathematics, Orr, Daniel D., Shimozono, Mark M., Matthews, Gretchen L. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Thesis |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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