I know that a von Neumann algebra on a separable Hilbert space can be (uniquely) decomposed into factors. But is there any non-trivial example showing how we can explicitly compute it?

Non-trivial: I mean it is not a factor itself, it is not abelian or of finite dimension.

I know that a von Neumann algebra on a separable Hilbert space can be (uniquely) decomposed into factors. But is there any non-trivial example showing how we can explicitly compute it?

Non-trivial: I mean it is not a factor itself, not abelian or of finite dimension.

I know that a von Neumann algebra on a separable Hilbert space can be (uniquely) decomposed into factors. But is there any non-trivial example showing how we can explicitly compute it?

Non-trivial: I mean it is not a factor itself and it is not abelian.

I know that a von Neumann algebra on a separable Hilbert space can be (uniquely) decomposed into factors. But is there any non-trivial example showing how we can explicitly compute it?

Non-trivial: I mean it is not a factor itself, it is not abelian or of finite dimension.