We define the affinization of an arbitrary monoidal category C, corresponding to the
category of C-diagrams on the cylinder. We also give an alternative characterization
in terms of adjoining dot generators to C. The affinization formalizes and unifies many
constructions appearing in the literature. In particular, we describe a large number
of examples coming from Hecke-type algebras, braids, tangles, and knot invariants.
When C is rigid, its affinization is isomorphic to its horizontal trace, although the two
definitions look quite different. In general, the affinization and the horizontal trace are
not isomorphic.
We then use the affinization to show our main result, which is an explicit isomorphism
between the central charge k reduction of the universal central extension of the
elliptic Hall algebra and the trace, or zeroth Hochschild homology, of the quantum
Heisenberg category of central charge k. We use this isomorphism to construct large
families of representations of the universal extension of the elliptic Hall algebra.
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/44133 |
| Date | 04 October 2022 |
| Creators | Mousaaid, Youssef |
| Contributors | Savage, Alistair |
| Publisher | Université d'Ottawa / University of Ottawa |
| Source Sets | Université d’Ottawa |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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