The composition series of ideals of the partial-isometric crossed product by the semigroup $\mathbb{N}^{2}$

Abstract

Suppose that N 2 is the positive cone of the abelian lattice-ordered group Z 2 , and α an action of N 2 by extendible endomorphisms of a C * -algebra A. Let A × piso α N 2 be the partial-isometric crossed product by the endomorphic action α. A composition series 0 ≤ L 1 ≤ L 2 ≤ A × piso α N 2 of essential ideals is obtained for which we identify the subquotients with familiar algebras.