The Classification of Limits of2n-cycle Algebras

We obtain a complete classification of the locally finite algebras A0 = ͢alg lim Ak and the operator algebras A = ͢lim Ak associated with towers A1 ≤ A2 ≤ A3 ... consisting of 2n-cycle algebras, where n ≥ 3, with the inclusions of rigid type. The complete isomorphism invariant is essentially the triple (K0(A), H1(A), ∑(A)) where K0(A) is viewed as a scaled ordered group, H1(A) is partial isometry homology group and ∑(A) ≤ K0(A) H1(A) is the 2n-cycle joint scale.