Unitriangular matrix group:UT(3,C)

Definition
This group is defined as the member of family::unitriangular matrix group of degree three over the field of complex numbers. Explicitly, it is the following group of matrices under multiplication:

$$\left \{ \begin{pmatrix} 1 & a & b \\ 0 & 1 & c \\ 0 & 0 & 1 \\\end{pmatrix} \mid a,b,c \in \mathbb{C} \right \}$$

Structures

 * The group has the natural structure of an algebraic group over the field of complx numbers. As an algebraic group, it is a unipotent algebraic group.
 * The group has the structure of a complex Lie group (and hence also a topological group). The underlying complex-analytic manifold is equivalent to $$\mathbb{C}^3$$.