Some inverse limit approaches to the Riordan group

Using the inverse limit tool, we obtain the Riordan group in its infinite and bi-infinite representations from groups of finite Riordan matrices. We define two different reflections for bi-infinite Riordan matrices. Employing these definitions, we give answers to the problems D⊥=DD⊥=D and D⋄=DD⋄=D in the Riordan group. So, we describe the self-complementary and self-dual Riordan matrices.