Nilpotent extensions and entire cyclic cohomology
The author shows that a \(C\)-split of Banach algebras \(0 \to I \to E \to A \to 0\) \((I\) is a nilpotent ideal) induces an isomorphism \(HE^* (A) \to HE^*(E)\) in the entire cyclic cohomology. The proof is based on the following principle [\textit{J. Cuntz} and \textit{D. Quillen}, ``Operators on noncommutative differential forms and cyclic homology'' (to appear), ``Algebra extensions and nonsingularity'' (to appear), ``Cyclic homology and nonsingularity'' (to appear)]: -- under some conditions, a linear map between algebras \(f : A \to B\) induces a functorial ``Connes-Chern character'' map \(Ch(f) : H^* (B) \to H^* (A)\) \((H^*\) is either the periodic or the entire cyclic cohomology functor).
scientific article; zbMATH DE number 682606