Singularity of radial subalgebras in II 1 factors associated with free products of groups

Abstract

Let G be the free product of N groups each having order k ⩽ N and let A be the maximal abelian subalgebra of the group von Neumann algebra L ( G), called the radial algebra of G. The Pukánszky invariant of the abelian algebra A =( A ∨ JAJ)″ is computed in this case. If N ⩾ 3, A is isomorphic to A ⊕ ( A ⊗ A) and A is singular. If N = k = 2, A is isomorphic to A ⊕ A and A is a Cartan subalgebra.