Title: Isomorphism between quantum and classical $sl(n)$
Speaker: Sachin Gautam (Ohio State University)
Abstract: Quantum groups, introduced by Drinfeld and Jimbo, are Hopf algebras naturally associated to simple Lie algebras. For a simple Lie algebra $g$, the quantum group $\mathcal{U}_h(g)$ is known to be isomorphic, as an algebra, to the enveloping algebra $\mathcal{U}(g)\big[\big[h\big]\big]$ (where $h$ is a formal variable). This isomorphism exists due to a non-trivial cohomological argument and has only been written down for $g=sl(2)$ by Drinfeld and Chari-Pressley. In this talk, I will give an explicit formula resulting in such an isomorphism between $\mathcal{U}_h(sl(n))$ and $\mathcal{U}(sl(n))\big[\big[h\big]\big]$ for every $n$ greater than or equal to 2. This is a recent joint work with Andrea Appel (arxiv:1712.03601).
Seminar URL: https://research.math.osu.edu/reps/