I’m working on some group-theoretic stuff related to *n* copies of a unital quantum channel and am in search of some isomorphism between the dihedral group and the unitary group U(*n*).

Now, what’s interesting is that the unitary group U(1) is isomorphic to the circle group, i.e. the geometric circle, while can be thought of as representing the discrete rotations of an *n*-gon. So one would think that as , would become isomorphic to U(1) since the *n*-gon geometrically approaches a circle. But is isomorphic to which geometrically is a line infinite in both directions.

Technically, for what I’m interested in, I suspect U(1) would be too restrictive anyway. I’m more interested in finding a direct isomorphism between and U(*n*) or, at the very least, something broader than U(1) and, preferably, broader than SU(2) as well.

So if you’re a regular reader of this blog and you know of any such isomorphism, post it here!