A new construction of factors of type $\mathrm{II}{\mathrm{I}}_1$

Abstract

We give in this paper a new construction of factors of type $\mathrm{II}{\mathrm{I}}_1$. Under certain assumptions, we can, thanks to a result by Popa, give a complete classification for this family of factors. Although these factors are never full, we can nevertheless, in many cases, compute Connes' $\tau$ invariant. We obtain a new example of an uncountable family of pairwise non-isomorphic factors of type $\mathrm{II}{\mathrm{I}}_1$ with the same $\tau$ invariant.

22 pages

References in corpus (3)

• Some prime factorization results for type II_1 factors
• On multiplicity and free absorption for free Araki-Woods factors
• On Ozawa's Property for Free Group Factors

Cited by in corpus (1)

• Fullness and Connes' $\mathbf{\tau }$ invariant of type III tensor product factors