2001/10/15 by Maria Grazia Viola, Viola, Maria Grazia
Mathematics · #46L37 #46L40 #46L54 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:46L37 #msc:46L40 #msc:46L54
paper · pdf · doi:10.48550/arxiv.math/0110158
21 pages, Latex, corrected typos, add a couple of remarks in the preliminary section
openalex publication_date 2001/10/15 · arxiv created 2004/07/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a subfactor construction for a II1 factor M which is not anti-isomorphic to itself. The II1 factor we consider is essentially the same as the example previously given by Connes. However, our construction uses the recently developed theory of free group factors. We show that there exists an inclusion of II1 factors A⊂ B which by iteration of the Jones basic construction produces M as the enveloping algebra. Here A is a free group factor and B is isomorphic to the crossed product of A by an action of a finite group. By using a Connes' argument involving the invariant χ(M), we verify that M is not anti--isomorphic to itself. Publication of this manuscript is funded in part by the National Science Foundation. This material is based upon work supported by the National Science Foundation under Grant No. DMS--9810361.