Metasymmetry and Volichenko algebras

We continue the study of a generalization of supermanifolds (called here metamanifolds) on which “functions” form a metabelian algebra (one for which [[x, y], z] = 0). The usual superspaces considered as metaspaces and some conventional lagrangeans have a symmetry wider than supersymmetry. Infinitesimal transformations of these metaspaces constitute Volichenko algebras. The Volichenko algebras are natural generalizations of Lie superalgebras. Here we classify simple finite-dimensional complex Volinchenko algebras (under a technical hypothesis). Their list is as discrete as the list of simple Lie superalgebras. The results may be significant for applications to physics in connection with parastatistics.