Finitely generated nilpotent group C*-algebras have finite nuclear dimension

We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra $A$ generated by an irreducible representation of such a group has decomposition rank at most 3. If, in addition, $A$ satisfies the universal coefficient theorem, another string of deep results shows it is classifiable by its Elliott invariant and is approximately subhomogeneous. We give a large class of irreducible representations of nilpotent groups (of arbitrarily large nilpotency class) that satisfy the universal coefficient theorem and therefore are classifiable and approximately subhomogeneous.Comment: Fixed typos. Question 5.1 of the previous version was already answered in the literature; we have provided the appropriate referenc

Evaluating Leadership Development Through Experiential Learning In A Virtual Environment

The strategic leadership center of a senior military service college collaborated with an elite law school to provide leadership development to senior law school students. The focus was an International Strategic Crisis Negotiation Exercise set in the South China Sea. Due to an unexpected global health pandemic the course was forced online to a virtual environment. The strategic leadership center gathered data from volunteer students and their mentors to determine the impact of the virtual setting. Using four archival datasets, a program evaluation was conducted using a case study methodology to determine the effectiveness of experiential learning through simulation in a virtual environment and to gain an in-depth understanding of its impact on the development of the leadership soft skills of teamwork, communication, and negotiation techniques for senior law school students from the perspective of students and their mentors. The research study found that experiential learning through simulation in a virtual environment was highly effective and transformative. The interpretation of the ten findings is enlightening and contributes to a more complete understanding of experimental learning. The significance of the study is its contribution to leadership education, legal education, and education policies

Rigidity and Nonrigidity of Corona Algebras

Shelah proved in the 1970s that there is a model of ZFC in which every homeomorphism of the Cech-Stone remainder of the natural numbers is induced by a function on the natural numbers. More recently, Farah proved that in essentially the same model, every automorphism of the Calkin algebra on a separable Hilbert space must be induced by a linear operator on the Hilbert space. I will discuss a common generalization of these rigidity results to a certain class of C*-algebras called corona algebras. No prerequisites in C*-algebra will be assumed

Forcing axioms and coronas of nuclear C∗C^*-algebras

We prove several rigidity results for various large classes of corona algebras, assuming the Proper Forcing Axiom. In particular, we prove that a conjecture of Coskey and Farah holds for all separable $C^*$-algebras with the metric approximation property and an increasing approximate identity of projections.Comment: 56 page