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

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