Structure of deformed $w_{1+\mathrm{\infty }}$ symmetry and topological generalization in Celestial CFT

We investigate a deformation of $w_{1+\mathrm{\infty }}$ algebra recently introduced in arxiv:2111.11356 in the context of Celestial CFT that we denote by ${\tilde{W}}_{1+\mathrm{\infty }}$ algebra. We obtain the operator product expansions of the generating currents of this algebra and explore its supersymmetric and topological generalizations.