Quasi homomorphismes, cohomologie cyclique et positivité. (Quasi homomorphisms, cyclic cohomology and positivity) (Q1114906)

The aim of this paper is to show that the cyclic cohomology of an algebra A, associated by the construction given by the first author in the paper ``Non-commutative differential geometry''. Publ. Math., Inst. Hautes Etud. Sci. 62, 41-144 (1985; Zbl 0592.46056) to any homomorphism of the universal algebra qA of the second author in an algebra \(J=L^ p(h^+)\) (the Schatten ideal of p-summable operators on \(h^+)\) equipped with a trace of the suitable domain of \(J^ n\), is obtained by this construction. When A is a \(C^*\)-algebra, so is qA and the authors prove that the notion of positive trace makes sense and it defines a type I or II Fredholm module on A; a notion of positivity for cyclic cocycles is obtained and examplified.