Partially ordered groups
Copyright policy )Partially ordered groups
The importance of partially ordered (po-) groups for the theory of operator algebras, particularly \(C^*\)-algebras, is explained. If \(A\) is an \(AF\)-algebra then \(K_ 0(A)\) is a po-group which can be used to analyse and classify \(A\). On the other hand, given a po-group, one can associate to it a certain universal \(C^*\)-algebra which in particular cases turns out to be the \(C^*\)-algebra generated by the Toeplitz operators with continuous symbols on the dual group. The author discusses, in some detail, three subclasses of po-groups, namely: totally (fully) ordered groups, Archimedean groups and dimension groups.
dimension groups, totally ordered groups, Archimedean groups, \(C^*\)-algebras, \(AF\)-algebra, \(K\)-theory and operator algebras (including cyclic theory), Ordered groups, partially ordered groups, operator algebras
dimension groups, totally ordered groups, Archimedean groups, \(C^*\)-algebras, \(AF\)-algebra, \(K\)-theory and operator algebras (including cyclic theory), Ordered groups, partially ordered groups, operator algebras
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