I am learning about semisimple algebraic groups, and came across the concept of Chevalley groups.
I think it is very exciting that you can define all semisimple complex linear algebraic groups over $\mathbb{Z}$ because then you can extend scalars to a finite field $\mathbb{F}_p$ and obtain a finite group, etc. (at least for all large enough $p$).
What I don't know is a single example of a semisimple complex linear algebraic group $G$ where it's not obvious that $G$ can be defined by polynomials with coefficients in $\mathbb{Z}$. Several examples would be ever nicer to have.
Here are obvious examples: special linear groups, symplectic groups, special orthogonal groups.
What are some less obvious examples? (i.e. examples where the "standard" definition is not given by integer defining polynomials).
I know that there's a classification of semisimple algebraic groups, relying eventually on Dynkin diagrams, so I tried looking this up to find examples, but didn't come up with anything interesting in the context of my question above.