The Hopf algebra structure of the h-deformed Z(3)-graded quantum supergroup GL(h,j)(1|1)

In this work, we define a new proper singular g matrix to construct a Z(3)-graded calculus on the h-deformed quantum superplane. Using the obtained calculus, we construct a new h-deformed Z(3)-graded quantum supergroup and give some features of it. Finally, we build up the Hopf algebra structure of this supergroup.