Fractional supersymmetric su(2) algebras

Abstract

In this paper, the third root of the Lie algebra su(2) based on the permutation group S3 is formulated in the Hopf algebra formalism.

The Real Forms of the Fractional Supergroup SL(2,C)

“…When we compare our results with [23,25,26], we find that we obtained consistent results because the fractional supergroup SU( 2) is dual to the fractional superalgebra su(2) given in [26]. Moreover, the definitions in [23,25] are consistent with the fractional supergroups A N 3 (SU(1, 1)) and A N 3 (SL(2, R)) obtained here.…”

“…As is known, one can pass from Lie algebras to Lie groups by an exponential map. However, this transition is not always possible, or it may be difficult, but with algebraic approaches, transitions between algebras and groups are easier [1,19,[23][24][25][26]. For example, the supergroup and fractional supergroup definitions, which are the duals of the superalgebras and fractional superalgebras, have been defined with the algebraic approaches in [23].…”