descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 1999Embargo end date: 01 Jan 1998 English Publisher:Indiana University Mathematics JournalJournal:Indiana University Mathematics Journal, volume 48, pages 0-0 (issn: 0022-2518,

Authors: Donsig, Allan P.; Power, S. C.;

doi: 10.1512/iumj.1999.48.1688 , 10.48550/arxiv.math/9810123

arXiv: http://arxiv.org/abs/math/9810123

The classification of limits of 2n-cycle algebras

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Abstract

We obtain a complete classification of the locally finite algebras and the operator algebras, given as algebraic inductive limits and Banach algebraic inductive limits respectively, of direct systems: A_1 contained in A_2 contained in A_3 and so on. Here the A_k are 2n-cycle algebras, where n is at least 3 and the inclusions are of rigid type. The complete isomorphism invariant is essentially the triple (K_0(A), H_1(A), Sigma(A)) where K_0(A) is viewed as a scaled ordered group, H_1(A) is a partial isometry homology group and Sigma(A), contained in the direct sum of K_0(A) and H_1(A), is the 2n-cycle joint scale.

14 pages

Related Organizations

University of Nebraska-Lincoln
United States
Lancaster University
United Kingdom

Keywords

limit algebras, Mathematics - Operator Algebras, \(K\)-theory and operator algebras (including cyclic theory), locally finite algebras, inductive limits, \(K\)-theory, 47D25; 46K50, 510, Classifications of \(C^*\)-algebras, classification, Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.), FOS: Mathematics, partial isometry homology group, Operator Algebras (math.OA), 47D25, 46K50

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Algebraic isomorphisms of limit algebras
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