M.Sc Thesis

M.Sc StudentShapiro Gregory
SubjectAmenable Algebras and Ends of Algebras
DepartmentDepartment of Mathematics
Supervisors PROF. Amos Nevo
PROF. Michah Sageev


In this work we will discuss a notion of amenability and related subjects like property T, a-T-amenability, amenable representations, and ends of algebras.

In the first part of this work we will discuss definitions of amenable algebras in case of algebras with zero divisors. In this part we will prove that for general affine algebra amenability is equivalent to no paradoxality and to existence of finite left invariant dimensional measure. In this part we will also provide an application of amenable algebras to the zero divisors conjecture.

In the second part of our work we will focus on group algebras and amenable group representations. We will prove that group algebra is amenable if an only if a group is amenable. In this part we will also prove the equivalence between "amenable representations" and "algebraically amenable representations" for representations on homogeneous spaces.

In the third (and last) part of our work we will study ends of Γ modules. In this part we will present a connection between existence of nontrivial ends of Γ modules and a-T-amenability of the corresponding group.