SINGULARITY OF RADIAL SUBALGEBRAS IN II1-FACTORS ASSOCIATED WITH FREE-PRODUCTS OF GROUPS

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. © 1992.