Some algebraic features of \(\mathbb{Z}_2\)-graded \(KK\)-theory
The aim of this article is to study the connection of the author's version of Kasparov's \(\mathbb{Z}_2\)-graded \(KK\)-functor and the graded Kasparov's Ext-functor. One of the main results is a new construction of the Kasparov product for the graded \(KK\)-functor. The generalizations to \(\mathbb{Z}_2\)-graded \(C^*\)-algebras of the universal coefficient theorem, the Künneth theorems for \(KK_* (A,B)\) and \(K_* (A\otimes B)\), and the Thom isomorphism theorem are obtained. The methods of this paper are closely connected with Cuntz's approach in the ungraded case.
\(\mathbb{Z}_2\)-graded \(C^*\)-algebras
scientific article; zbMATH DE number 1132938