Elsevier

Physics Letters B

Volume 252, Issue 1, 6 December 1990, Pages 91-96
Physics Letters B

Metasymmetry and Volichenko algebras

https://doi.org/10.1016/0370-2693(90)91086-QGet rights and content

Abstract

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.

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    Present address: Department of Mathematics, Yale University, Box 2155 Yale Station, New Haven, CT 06520, USA.

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