In Quantum Physics one often has to deal with commutators.
Here I want to denote by $H_0$ the set of all hermitian matrices with trace equal to zero! One can easily relate it to $\mathfrak{su}(N)=iH_0.$
Now, my question is basically if there has been a detailed study of the centralizer in $H_0$ or $\mathfrak{su}(N)$ somewhere?
I am particularly interested in questions like: Given a set of matrices $S$ spanning sum subspace of $H_0$ what is known about the centralizer
$C_{H_0}(S):=\{A \in H_0; [A,B]=0 \text{ for all B in } H_0\}$
Can we classify it in its dimension?
I am not really sure where I could find such a reference, but due to its relationship to $\mathfrak{su}(N)$ I thought that this should have been already studied somewhere.