A Unique Prime Decomposition Result for Wreath Product Factors

Abstract

We use malleable deformations combined with spectral gap rigidity theory, in the framework of Popa's deformation/rigidity theory to prove unique tensor product decomposition results for II${}_1$ factors arising as tensor product of wreath product factors. We also obtain a similar result regarding measure equivalence decomposition of direct products of such groups.

8 pages

References in corpus (5)

• W*-superrigidity for group von Neumann algebras of left-right wreath products
• Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups
• Some $OE$ and $W^{\ast }$-rigidity results for actions by wreath product groups
• L^2-rigidity in von Neumann algebras
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Cited by in corpus (8)

• Unique prime factorization and bicentralizer problem for a class of type III factors
• Primeness results for von Neumann algebras associated with surface braid groups
• On fundamental groups of tensor product $\mathrm{I}{\mathrm{I}}_1$ factors
• Tensor product decompositions of II${}_1$ factors arising from extensions of amalgamated free product groups
• Prime II${}_1$ factors arising from irreducible lattices in products of rank one simple Lie groups
• Product rigidity in von Neumann and C${}^{\ast }$-algebras via s-malleable deformations
• Classification of Tensor Decompositions of II${}_1$ Factors Associated With Poly-Hyperbolic Groups
• Classification of tensor decompositions for II${}_1$ factors