Fermionic Generalization Of Lineal Gravity In Centrally Extended Formulation (original) (raw)

We generalize the central extension of the (1 + 1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but special graded algebra containing in the right hand side a central element only. We verify selfconsistency of Jacobi identities and derive the Casimir operator. Then we introduce the correspondent gauge fields and construct the classical gauge theory based on this graded algebra, present field transformations and derive the black hole mass in (1 + 1)-dimensions.