Hermite -polynomials and -oscillators
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all -Galois extensions up to homotopy equivalence in the case when is a Drinfeld-Jimbo quantum group.
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).