1212.1826 (Andrea Altomani et al.)

Classification of maximal transitive prolongations of super-Poincaré
algebras    [PDF]

Andrea Altomani, Andrea Santi

Let V be a complex orthogonal vector space and S an irreducible Cl(V)-module. A supertranslation algebra is a Z-graded Lie superalgebra $m=m_{-2}+m_{-1}=V+(S+...+S)$ whose bracket $[.,.]|_{m_{-1}\otimes m_{-1}$ is so(V)-invariant and non-degenerate. We consider the maximal transitive prolongations in the sense of Tanaka of supertranslation algebras. We prove that they are finite-dimensional for dim V\geq 3 and classify them in terms of super-Poincar\'e algebras and appropriate Z-gradations of simple Lie superalgebras.

View original: http://arxiv.org/abs/1212.1826