The Classification of Limits of 2n-cycle Algebras
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: A1 contained in A2 contained in A3 and so on. Here the Ak 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 (K0(A), H1(A), Sigma(A)) where K0(A) is viewed as a scaled ordered group, H1(A) is a partial isometry homology group and Sigma(A), contained in the direct sum of K0(A) and H1(A), is the 2n-cycle joint scale.
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