  We investigate the algebro-geometric structure of a novel two-parameter
quantum deformation which exhibits the nature of a semidirect or cross-product
algebra built upon GL(2) x GL(1), and is related to several other known
examples of quantum groups. Following the R-matrix framework, we construct the
L+/- functionals and address the problem of duality for this quantum group.
This naturally leads to the construction of a bicovariant differential calculus
that depends only on one deformation parameter, respects the cross-product
structure and has interesting applications. The corresponding Jordanian and
hybrid deformation is also explored.
