We describe a class of rank-2 graphs whose C∗-algebras are AT algebras. For a subclass which we call rank-2 Bratteli diagrams, we compute the K-theory of the C∗-algebra. We identify rank-2 Bratteli diagrams whose C∗-algebras are simple and have real-rank zero, and characterise the K-invariants achieved by such algebras. We give examples of rank-2 Bratteli diagrams whose C∗-algebras contain as f...

1. Introduction IT is well known that there are a number of sets of axioms for Boolean algebra. In this paper, I give a set of five independent axioms using conditioned disjunction as the ternary operation which is postulated. The ternary operation is most naturally defined on the set 2 n —this is done in §2. The theorem is stated in §3 together with a slight generalization of this result; the ...

The Hausdorff–Alexandroff Theorem states that any compact metric space is the continuous image of Cantor’s ternary set C. It is well known that there are compact Hausdorff spaces of cardinality equal to that of C that are not continuous images of Cantor’s ternary set. On the other hand, every compact countably infinite Hausdorff space is a continuous image of C. Here we present a compact counta...

We show that each irreducible tensor representation of weight 2 the rotation group in space rank 3 tensors over three-dimensional gives rise to an associative algebra with unity. find algebraic conditions be satisfied by generators these algebras. Part relations is binary, and another part ternary type. The structure latter one based on use cyclic [Formula: see text] generated primitive cubic r...

We propose a generalization of non-commutative geometry and gauge theories based on ternary Z3-graded structures. In the new algebraic structures we define, we leave all products of two entities free, imposing relations on ternary products only. These relations reflect the action of the Z3-group, which may be either trivial, i.e. abc = bca = cab, generalizing the usual commutativity, or non-tri...