3 J an 2 00 7 On a ” New ” Deformation of GL ( 2 )

We refute a recent claim in the literature of a " new " quantum deformation of GL(2). Until the year 2000 it was not clear how many distinct quantum group deformations are admissible for the group GL(2) and the supergroup GL(1|1). For the group GL(2) there were the well-known standard GL pq (2) [1] and nonstandard (Jordanian) GL gh (2) [2] two-parameter deformations. (The dual quantum algebras of GL pq and GL gh were found in [3] and [4], respectively.) For the supergroup GL(1|1) there were the standard GL pq (1|1) [5, 6, 7] and the hybrid (standard-nonstandard) GL qh (1|1) [8] two-parameter deformations. Then, in the year 2000 in [9] it was shown that the list of these four deformations is exhaustive (refuting a long standing claim of [10] (supported also in [11, 12]) for the existence of a hybrid (standard-nonstandard) two-parameter deformation of GL(2)). In particular, it was shown that the above four deformations match the distinct