C*-algebras associated with endomorphisms of groups

In 2002, Ilan Hirshberg defined a C -algebra associated with endomorphisms of abelian groups with finite cokernel. In fact, it was a starting point of new constructions associating C -algebras to simple objects like groups, semigroups and rings. In this book, we present a natural continuation of that work, we construct the same C -algebra for endomorphisms with infinite cokernel. We use the subset structure of the group to index interesting projections in the C -algebra and present interesting connections with the semigroup C -algebras defined by Xin Li. We also calculate some K-groups associated to such constructions.

Autorentext

Felipe Vieira, Ph.D.: Mathematics at Westfälische Wilhelms-Universität Münster, Germany. Lecturer and Researcher at the Department of Mathematics, Universidade Federal de Santa Catarina, Blumenau, Brazil.

Klappentext

In 2002, Ilan Hirshberg defined a C-algebra associated with endomorphisms of abelian groups with finite cokernel. In fact, it was a starting point of new constructions associating C-algebras to simple objects like groups, semigroups and rings. In this book, we present a natural continuation of that work, we construct the same C-algebra for endomorphisms with infinite cokernel. We use the subset structure of the group to index interesting projections in the C-algebra and present interesting connections with the semigroup C*-algebras defined by Xin Li. We also calculate some K-groups associated to such constructions.