• Corpus ID: 119584958

A new construction of factors of type ${\rm III_1}$

  title={A new construction of factors of type \$\{\rm III\_1\}\$},
  author={Cyril Houdayer},
  journal={arXiv: Operator Algebras},
  • Cyril Houdayer
  • Published 9 January 2006
  • Mathematics
  • arXiv: Operator Algebras
We give in this paper a new construction of factors of type ${\rm III_1}$. 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 ${\rm III_1}$ with the same $\tau$ invariant. 


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