Type ${\rm III_1}$ factors generated by regular representations of infinite dimensional nilpotent group $B_0^{\mathbb N}$

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

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…

Linear dynamical systems of nilpotent Lie groups

We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the representation space, or the complement of the set of regular points is dense, and then the interior of that complement is either empty or dense in the representation space. The regular points are by definition the points whose orbits are locally compact in their relative topology. We thus generalize some results from the recent literature on linear actions of ab…

正则2步 nilpotent 群主符号的 Toeplitz 群场

Fields of Toeplitz algebras form the principal symbol of regular 2-step nilpotent groups

该研究通过连续 Toeplitz 群场和交叉乘积恢复正则2步 nilpotent 群的C*-代数，并推广到多接触流形及H型群模型的流形。

Normal Limits of Nilpotents in C*-Algebras

We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with separable predual and for unital, simple, purely infinite C*-algebras. Some restrictions that prevent normal operators from being limits of quasinilpotent operators will be given. The case of AF C*-algebras will be of particular interest. In addition, the closure of the span of the nilpotent operators and the distance from a projection to the nilpotent opera…