Generalizing the $\mathfrak{bms}_{3}$ and 2D-conformal algebras by expanding the Virasoro algebra

Abstract

By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $\mathfrak{bms}_{3}$ algebra are obtained from the Virasoro algebra. We extend this result to construct new families of expanded Virasoro algebras that turn out to be infinite dimensional lifts of the so-called $\mathfrak{B}_{k}$, $\mathfrak{C}_{k}$ and $\mathfrak{D}_{k}$ algebras recently introduced in the literature in the context of (super)gravity. We also show how some of these new infinite-dimensional symmetries can be obtained from expanded Ka\v{c}-Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.