ON A HOPF ALGEBRA RELATED TO THE GLq(2) AND GLp,q(2) QUANTUM GROUPS

Abstract

By adding one extra generator with the standard GL q(2) quantum group, we construct a Hopf algebra [Formula: see text] which depends on two deformation parameters and five generators. Curiously, it turns out that there exists a nonlinear realization of the two-parameter deformed GL p,q(2) quantum group through generators of this [Formula: see text] algebra. Subsequently, we find the invariant noncommutative planes associated with the [Formula: see text] quantum group and also discuss how the well-known Manin planes corresponding to the GL p,q(2) quantum group can be produced automatically, through such construction. Finally, we consider the “colored” extension of the GL p,q(2) quantum group as well as corresponding noncommutative planes and explore their intimate connection with the “colored” extension of [Formula: see text] Hopf structure.