<div> We introduce the quantum toroidal superalgebra E<sub>m|n </sub>associated with the Lie superalgebra gl<sub>m|n</sub> and initiate its study. For each choice of parity "s" of gl<sub>m|n</sub>, a corresponding quantum toroidal superalgebra E<sub>s</sub> is defined. </div><div> </div><div><br></div><div>To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. </div><div><br></div><div>The superalgebra E<sub>s</sub> contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra U<sub>q</sub> sl̂<sub>m|n</sub> with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of E<sub>s</sub>, which exchanges the vertical and horizontal subalgebras.</div><div><br></div><div>If <i>m</i> and <i>n</i> are different and "s" is standard, we give a construction of level 1 E<sub>m|n</sub>-modules through vertex operators. We also construct an evaluation map from E<sub>m|n</sub>(q<sub>1</sub>,q<sub>2</sub>,q<sub>3</sub>) to the quantum affine algebra U<sub>q</sub> gl̂<sub>m|n</sub> at level c=q<sub>3</sub><sup>(m-n)/2</sup>.</div>
| Identifer | oai:union.ndltd.org:purdue.edu/oai:figshare.com:article/12201407 |
| Date | 30 April 2020 |
| Creators | Luan Pereira Bezerra (8766687) |
| Source Sets | Purdue University |
| Detected Language | English |
| Type | Text, Thesis |
| Rights | CC BY-NC-SA 4.0 |
| Relation | https://figshare.com/articles/Quantum_Toroidal_Superalgebras/12201407 |
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