The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$

Details The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$ The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$

2009-07-27

arxiv.org/abs/0907.4645v1

Mathematics

Operator Algebras

Scientific paper

We study the von Neumann algebra, generated by the regular representations of the infinite-dimensional nilpotent group $B_0^{\mathbb Z}$. 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 $B_0^{\mathbb Z}$ is the type ${\rm III}_1$ hyperfinite factor. We use a technique, developed in [20] where a similar result was proved for the group $B_0^{\mathbb N}$. 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 ${\rm III_1}$ factors generated by regular representations of infinite dimensional nilpotent group $B_0^{\mathbb N}$, arXiv:0803.3340v1.

Affiliated with

Also associated with

No associations

Rating

The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The type ${\rm III_1}$ factor generated by regular representations of the infinite dimensional nilpotent group $B_0^\mathbb Z$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-246150