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 (G), called the radial algebra of G. The Pukánszky invariant of the abelian algebra =(A ∨ JAJ)″ is computed in this case. If N ⩾ 3, is isomorphic to A ⊕ (A ⊗ A) and A is singular. If N = k = 2, is isomorphic to A ⊕ A and A is a Cartan subalgebra.
Boca, F., Radulescu, F. (1992). Singularity of radial subalgebras in II1 factors associated with free products of groups. JOURNAL OF FUNCTIONAL ANALYSIS, 103(1), 138-159 [10.1016/0022-1236(92)90139-A].
Singularity of radial subalgebras in II1 factors associated with free products of groups
RADULESCU, FLORIN
1992-01-01
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 (G), called the radial algebra of G. The Pukánszky invariant of the abelian algebra =(A ∨ JAJ)″ is computed in this case. If N ⩾ 3, is isomorphic to A ⊕ (A ⊗ A) and A is singular. If N = k = 2, is isomorphic to A ⊕ A and A is a Cartan subalgebra.File in questo prodotto:
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