Project acronym: ToDyRiC
Project full title: Topological Dynamics of Rings and C*-algebras
Grant agreement no.: 267079
Duration: January 2011 until December 2015

Principal Investigator: Prof. Dr. Joachim Cuntz

Team Members:  Prof. Dr. Xin Li / Dr. Bhishan Jacelon

Host Institution: Westfaelische Wilhelms-Universitaet Muenster



Proposal summary 
This project is concerned with problems in several areas. A starting point is the new concept of a ring C*-algebra associated with a countable ring without zero divisors. For special rings this C*-algebra has a very rich and surprising structure. A particularly interesting case is the ring of algebraic integers in a global field. In this context the algebra contains well known topological dynamical systems. We plan to use the analysis of ring algebras and of similar algebras as an organizing  principle for the study of many questions in C*-algebra theory, K-theory, ergodic theory and number theory. Some of these questions are well known and very difficult.

J. Cuntz:  

Quillen's work on the foundations of cyclic cohomology

J. Cuntz / C. Deninger / M. Laca:

C*-algebras of Toeplitz type associated with algebraic number fields

J. Cuntz / S. Echterhoff / X. Li:

K-theory for semigroup C*-algebras

J. Cuntz / A. Vershik:

C*-algebras associated with endomorphisms and polymorphisms of compact Abelian groups

B. Jacelon:

X. Li:

K-theory for ring C*-algebras attached to function fields with only one infinite place

Nuclearity of semigroup C*-algebras and the connection to amenability

Semigroup C*-algebras and amenability of semigroups

X. Li / W. Lück:

K-theory for ring algebras - The case of number fields with higher roots of unity

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