Braided structure of fractionalZ 3-supersymmetry

It is shown that fractionalZ ₃-superspace is isomorphic to theqexp(2/3i) limit of the braided line.Z ₃-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its associated covariant derivative emerge as theqexp(2/3i) limits of the left and right derivatives from the calculus on the braided line.Presented at the 5th International Colloquium on Quantum Groups: Quantum Groups and Integrable Systems, Prague, 20–22 June 1996.This paper describes research supported in part by E.P.S.R.C and P.P.A.R.C. (UK) and by the C.I.C.Y.T (Spain). J.C.P.B. wishes to acknowledge an FPI grant from the CSIC and the Spanish Ministry of Education and Science.