SU(2)

SU(2) is the symmetry of the weak force and has a base of 3 2*2 complex matrices with unit determinant;
((0,1),(1,0))
((0,-i),(i,0))
((1,0),(0,-1))
They all square to the unit matrix;
((1,0),(0,1))
SU(2) is like an extention to complex numbers.

SU(2) compares to E2/H2={,{}}/{,{,{}}} with the state quotient SE2/SH2=2/4=1/2.
Consider the collapsing iteration of H2;
{,{,{}}}
[,{,{}}]+[{,{}},]
[,[,{}]]+[,[{},]]+[[,{}],]+[[,{}],]
The collapse of {} gives only one state [], like +1-1=0.
H2 has a 2*2 form when collapsed, like a 2*2 matrix.
As I noted before, E2=H1={,{}} compares to Complex numbers.
{,{}}
[,{}]+[{},]
Thus E2/H2 is interpreted as "E2 for given H2".

Modular group has also 2*2 form and obeys a condition similar to unit determinant.
((a,b),(c,d)) with ad-bc=1.
DNA has a similar form with 2*2 bases.