Positive half of the Witt algebra acts on triply graded link homology

Abstract

The positive half of the Witt algebra is the Lie algebra spanned by vector fields $x^{m+1}\frac{d}{dx}$ acting as differentiations on the polynomial algebra $\mathbb{Q}[x]$ upon which the Soergel bimodule construction of triply graded link homology is based. We show that this action of Witt algebra can be extended to the link homology.