Normed groups and their applications in noncommutative differential geometry

A. A. Pavlov

Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Tome 266 (2000), pp. 234-244

Résumé

Our work is devoted to abstract study of so-called normed semi-groups, i.e., semi-groups having both rich topological and rich algebraic structure, which arise in some problems of non-commutative geometry. We consider in details the most interesting example, namely, an Abel semi-group $\mathscr N(A)$, where $A$ is a von Neumann algebra. The definition of this semi-group is based on the notion of stable equivalence of normal elements of $W^*$-algebras which generalizes the notion of stable equivalence of projectors.