My answer would be yes, the universe could be simply a mathematical abstraction.
Why? Because I have never heard about a proof that refutes your question (title). In fact, I've read in magazines -- a very long time ago (when the movie Matrix was popular) -- that we cannot refute the hypothesis that we live inside a simulation.
In other words: "the universe could be simply a mathematical abstraction" is a valid hypothesis. Today, we are unable to disprove it.
Regarding your other question (body - "can we create our own simulation?"): my answer would be no.
It has to do with the fact that it is computationally and physically impossible to run a simulation -- complete, perfect, lossless, bit precise -- of our universe from inside our universe (please someone verify that sentence, as I'm not 100% sure about that, it's just vague memory).
I'll quote myself (curiously, I've written down the following a few days ago):
The simulated beings will never have enough computational power to run a complete and perfect simulation like the simulation inside which they live.
Again, I might be completely wrong. But if I'm not wrong, I'll be very happy because I like that quote (I've written it down for a reason :)