Classification of the quantum deformation of the superalgebra GL(1|1)
Abstract
We present a classification of the possible quantum deformations of the supergroup
GL(1|1)
and its Lie superalgebra
gl(1|1)
. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each
R
matrix, one finds two inequivalent coproducts whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra
gl(1|1)
for suitable limits of the deformation parameters but this is no longer true in the unbraided case.