A description of amalgamated free products of finite von Neumann algebras over finite-dimensional subalgebras

We show that a free product of a II(1)-factor and a finite von Neumann algebra with amalgamation over a finite-dimensional subalgebra is always a II(1)-factor, and provide an algorithm for describing it in terms of free products (with amalgamation over the scalars) and compression/dilation. As an application, we show that the class of direct sums of finitely many von Neumann algebras that are interpolated free group factors, hyperfinite II(1)-factors, type I(n) algebras for n finite and finite-dimensional algebras, is closed under taking free products with amalgamation over finite-dimensional subalgebras.