ePrints

Cyclic-type cohomology of strict inductive limits of Fréchet algebras

Lookup NU author(s): Dr Zinaida LykovaORCiD

Downloads

Full text for this publication is not currently held within this repository. Alternative links are provided below where available.

Abstract

We present methods for the computation of the Hochschild and cyclic-type continuous homology and cohomology of some locally convex strict inductive limits A = lim→m Am of Fréchet algebras Am. In the pure algebraic case it is known that, for the cyclic homology of A, HCn = lim→m HCn(Am) for all n ≥ 0 [Cyclic Homology, Springer, Berlin, 1992, E.2.1.1]. We show that, for a locally convex strict inductive system of Fréchet algebras (Am)m=1∞ such that 0 → Am → Am+1 → Am+1/Am → 0 is topologically pure for each m and for continuous Hochschild and cyclic homology, similar formulas hold. For such strict inductive systems of Fréchet algebras we also establish relations between the continuous cohomology of A and Am, m ε N. For example, for the continuous cyclic cohomology ℋCn and ℋCn(Am), m ε N, we show the exactness of the following short sequence, for all n ≥ 0, 0 → limm←(1)ℋCn-1 (Am) → ℋCn(A) → limi← ℋCn (Am) → 0, where limm←(1) is the first derived functor of the projective limit. We give explicit descriptions of continuous periodic and cyclic homology and cohomology of a LF-algebra A = limm→Am which is a locally convex strict inductive limit of amenable Banach algebras Am, where for each m, Am is a closed ideal of Am+1. © 2005 Elsevier B.V. All rights reserved.

Publication metadata

Author(s): Lykova ZA

Publication type: Article

Publication status: Published

Journal: Journal of Pure and Applied Algebra

Year: 2006

Volume: 205

Issue: 3

Pages: 471-497

Date deposited: 28/04/2011

ISSN (print): 0022-4049

ISSN (electronic): 1873-1376

Publisher: Elsevier BV

URL: http://dx.doi.org/10.1016/j.jpaa.2005.07.014

DOI: 10.1016/j.jpaa.2005.07.014

Altmetrics

Share