arXiv subjects

Javad Mohammadkarimi

Publications and source records attributed to Javad Mohammadkarimi.

3 recordsLinked to original sources

arXiv2026

Pureness of Certain Crossed Product C*-Algebras

We establish comparison and divisibility properties for crossed product C*-algebras arising from automorphisms of algebras C (X, D) which lie over minimal homeomorphisms, from actions of compact groups which have finite Rokhlin dimension with commuting towers, and from actions of compact groups which have the restricted tracial Rokhlin property with comparison. We deduce that these crossed products we consider are pure, and conclude they have stable rank one, and in certain cases have real rank zero. We give examples in which these properties do not follow from previous results, in the case of C (X, D) due to the lack of Z-stability of D, the underlying topological spaces not being finite dimensional, or both.

math.OA↗

arXiv2025

Compact Group Actions with the Tracial Rokhlin Property II: Examples and Nonexistence Theorems

In a previous paper, we introduced the restricted tracial Rokhlin property with comparison, a ``tracial'' analog of the Rokhlin property for actions of second countable compact groups on infinite dimensional simple separable unital C*-algebras. In this paper, we give three classes of examples of actions of compact groups which have this property but do not have the Rokhlin property, or even finite Rokhlin dimension with commuting towers. One class consists of infinite tensor products of finite group actions with the tracial Rokhlin property, giving actions of the product of the groups involved. The second class consists of actions of the circle group on simple unital AT~algebras. The construction of the third class starts with an action of the circle on the Cuntz algebra ${\mathcal{O}}_{\infty}$ which has the restricted tracial Rokhlin property with comparison; by contrast, it is known that there is no action of this group on ${\mathcal{O}}_{\infty}$ which has finite Rokhlin dimension with commuting towers. We can then tensor this action with the trivial action on any unital purely infinite simple separable nuclear C*-algebra. One also gets such actions on certain purely infinite simple separable nuclear C*-algebras by tensoring the AT~examples with the trivial action on ${\mathcal{O}}_{\infty}$; these are different. We also discuss other tracial Rokhlin properties for actions of compact groups, and prove that there is no direct limit action of the circle group on a simple AF~algebra which even has the weakest of these properties.

math.OA↗

arXiv2022

Compact Group Actions with the Tracial Rokhlin Property

We define a "tracial" analog of the Rokhlin property for actions of second countable compact groups on infinite dimensional simple separable unital C*-algebras. We prove that fixed point algebras under such actions (and, in the appropriate cases, crossed products by such actions) preserve simplicity, Property (SP), tracial rank zero, tracial rank at most one, the Popa property, tracial Jiang-Su stability, Jiang-Su stability when the algebra is nuclear, infiniteness, and pure infiniteness. We also show that the radius of comparison of the fixed point algebra is no larger than that of the original algebra. Our version of the tracial Rokhlin property is an exact generalization of the tracial Rokhlin property for actions of finite groups on classifiable C*-algebras (in the sense of the Elliott program), but for actions of finite groups on more general C*-algebras it may be stronger. We discuss several alternative versions of the tracial Rokhlin property. We give examples of actions of a totally disconnected infinite compact group on a UHF algebra, and of the circle group on a simple unital AT algebra and on the Cuntz algebra ${\mathcal{O}}_{\infty}$, which have our version of the tracial Rokhlin property, but do not have the Rokhlin property, or even finite Rokhlin dimension with commuting towers.

math.OA↗