https://doi.org/10.1140/epjc/s10052-018-5739-7
Regular Article - Theoretical Physics
Generalizing the 
and 2D-conformal algebras by expanding the Virasoro algebra
1
Departamento de Matemática y Física Aplicadas, Universidad Católica de la Santísima Concepción, Alonso de Rivera, 2850, Concepción, Chile
2
Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaiso, Chile
3
Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, Viña del Mar, Chile
4
Facultad de Ingeniería y Ciencias and UAI Physics Center, Universidad Adolfo Ibáñez, Diagonal Las Torres 2640, Peñalolén, Santiago, Chile
* e-mail: patrick.concha@pucv.cl
Received:
1
September
2017
Accepted:
15
March
2018
Published online:
26
March
2018
By means of the Lie algebra expansion method, the centrally extended conformal algebra in two dimensions and the 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 
, 
and 
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.
© The Author(s), 2018
