Generalizing the $$\mathfrak {bms}_{3}$$ bms3 and 2D-conformal algebras by expanding the Virasoro algebra

Abstract

Abstract By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the $$\mathfrak {bms}_{3}$$ bms3 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 $$\mathfrak {B}_{k}$$ Bk , $$\mathfrak {C}_{k}$$ Ck and $$\mathfrak {D}_{k}$$ Dk 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 Kač–Moody algebras using modified Sugawara constructions. Applications in the context of three-dimensional gravity are briefly discussed.