\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
{W(a,b)} and {W(a,b;bar{a},bar{b})} are deformations of BMS3 and BMS4 algebra respectively. We present an {N}=2 supersymmetric extension of {W(a,b)} and {W(a,b;bar{a},bar{b})} in presence of R-symmetry generators that rotate the two supercharge generators. For {W(a,b)} our construction includes most generic central extensions of the algebra. In particular we show {N}=2 BMS3 algebra admits a new central extension.
For {W(a,b;bar{a},bar{b})}, we find that an infinite U(1)_V * U(1)_A extension of the algebra is not possible with linear and quadratic structure constants for generic values of the deformation parameters. This implies a similar constraint for U(1)_V * U(1)_A extension of {N}=2 , BMS4 algebra.
\end{document}