What are the fixed-points of the Y combinator?

Question

Since the Y combinator itself is a function (albeit a higher-order one), I was wondering what the fixed-points of Y itself are.

Answer 1

$U = λxλy·y(xy)$ is the fixed point of $Y$ and $Y$ is the fixed point of $U$.

How, and in what sense, I describe here: Equality Of (Infinitary) Lambda Terms.