On finite dimensional 2d fractional superalgebras

The formal definition of heterotic fractional supersymmetries (FS) (Q(-1/k) )(k) = P-1 is studied. Viewing FS as a finite dimensional subalgebras of th e ZF and Tye et al. FSC invariances, we propose more rigorous definitions o f these subalgebras. The Z(3) and Z(4) ZF parafermionic symmetries and the Level k = 4 Tye et al, ones are studied in details. Known results such as t he Leclair and Vafa fractional superalgebras are obtained as special cases. (C) 1999 Published by Elsevier Science B.V. All rights reserved.