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A special fermionic generalization of lineal gravity. (English) Zbl 1186.83119

Summary: The central extension of the \((1+1)\)-dimensional Poincaré algebra by including fermionic charges which obey not a supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We consider the algebra of generators, the field transformations and find the Lagrangian and the equation of motion, then we derive the Casimir operator and obtain the constant black hole mass.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C57 Black holes
81R05 Finite-dimensional groups and algebras motivated by physics and their representations
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