2009/07/27 by Ivan Dynov, Dynov, Ivan, Alexandre Kosyak +1
Mathematics · #22E65 #28C20 #43A80 #58D20 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Representation Theory (math.RT) #math.OA #math.RT #msc:22E65 #msc:28C20 #msc:43A80 #msc:58D20
paper · pdf · doi:10.48550/arxiv.0907.4645
arxiv created 2009/07/27 · openalex publication_date 2009/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the von Neumann algebra, generated by the regular representations of the infinite-dimensional nilpotent group B0\mathbb Z. In [14] a condition have been found on the measure for the right von Neumann algebra to be the commutant of the left one. In the present article, we prove that, in this case, the von Neumann algebra generated by the regular representations of group B0\mathbb Z is the type \rm III1 hyperfinite factor. We use a technique, developed in [20] where a similar result was proved for the group B0\mathbb N. The crossed product allows us to remove some technical condition on the measure used in [20]. [14] A.V. Kosyak, Inversion-quasi-invariant Gaussian measures on the group of infinite-order upper-triangular matrices, Funct. Anal. i Priloz. 34, issue 1 (2000) 86--90. [20] A.V. Kosyak, Type \rm III1 factors generated by regular representations of infinite dimensional nilpotent group B0\mathbb N, arXiv:0803.3340v1.