Banach cyclic (co)homology and the Connes-Tzygan exact sequence. (English) Zbl 0816.46076

Helemskii, A. Ya.

J. Lond. Math. Soc., II. Ser. 46, No. 3, 449-462 (1992).

An exact sequence which connects the cyclic (co)homology with the Hochschild, or simplicial, (co)homology was introduced by Connes for cohomology and by Tzygan for homology of abstract algebras with an identity. The first aim of this paper is to establish conditions for the existence of the Connes-Tzygan exact sequence for a given Banach algebra. The second aim is to use the Connes-Tzygan exact sequence to calculate Banach cyclic (co)homology of a certain class of Banach algebras.

Reviewer: V.Deundyak (Rostov-na-Donu)

MSC:

46M20	Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
46H05	General theory of topological algebras
55N35	Other homology theories in algebraic topology
46L80	\(K\)-theory and operator algebras (including cyclic theory)

Keywords:

cohomology; homology; Connes-Tzygan exact sequence; Banach algebra; Banach cyclic (co)homology