On the quantum symmetries associated with the two parameter free fermion model

Abstract

The quantum algebras associated with the R-matrix obtained from the two parameter free fermion model are examined. It is shown that in addition to Uq,s(gl(1, 1)) there exists another algebra which is isomorphic to Uq,s(gl(1, 1)) as an algebra but has a different Hopf structure. It does not have a classical limit and is related to Up(sl(2, c)) at a root of unity (p=i, i2=-1).