Special linear group:SL(2,R)

Definition
The group $$SL(2,\R)$$ is defined as the group of $$2 \times 2$$ matrices with entries from the field of real numbers and determinant $$1$$, under matrix multiplication.

$$SL(2,\R) := \left \{ \begin{pmatrix} a & b \\ c & d \\\end{pmatrix} \mid a,b,c,d \in \R, ad - bc = 1 \right \}$$.

It is a particular case of a member of family::special linear group over reals and hence of a member of family::special linear group.

Structures
The group has the structure of a topological group, a real Lie group, and an algebraic group restricted to the reals.

Elements
Below is a summary of the conjugacy class structure: