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The Classification of Limits of 2n-cycle Algebras

Allan P. Donsig·S. C. Power
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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.

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Allan P. Donsig, S. C. Power. 1998-10-19. The Classification of Limits of 2n-cycle Algebras. https://arxiv.org/abs/math/9810123

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