2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77333A classification is given for (regular) positions of direct sums of two matroid algebras (unital algebraic limits of matrix algebras) in a matroid superalgebra, where the individual summands have index 2 in their associated corner algebra. A similar classification is obtained for positions of direct sums of 2-symmetric algebras and, in the odd case, for the positions of sums of 2-symmetric C*-algebras in matroid C*-algebras. The approach relies on an analysis of intermediate non-self-adjoint operator algebras and the classifications are given in terms of K0 invariants, partial isometry homology and scales in the associated composite K0-homology group.28 pagesOperator Algebras46L35; 47D25text