THEK-THEORY OF SOME HIGHER RANK EXEL–LACA ALGEBRAS

Abstract

Let O be a higher rank Exel-Laca algebra generated by an alphabet A. If A contains d commuting isometries corresponding to rank d and the transition matrices do not have finite rows, then K 1 (O) is trivial and K 0 (O) is isomorphic to K 0 of the abelian subalgebra of O generated by the source projections of A.1991 Mathematics subject classification: 46L80, 46L55.

Some multidimensional Cuntz algebras

“…76 (2008) Some multidimensional Cuntz algebras 21 graph C * -algebras in [12]. On the other hand, the present work led us to the different approach in [2], [3] and [4].…”

On certain properties of Cuntz–Krieger-type algebras

“…This class, which is recalled in Section 2, includes (aperiodic) Cuntz-Krieger algebras [7], higher rank Exel-Laca algebras [5], (aperiodic) higher rank graph C * -algebras [8,9], (aperiodic) ultragraph algebras [13] and (cancelling) higher rank semigraph C * -algebras [2]. The aim of this note is to analyse these algebras further.…”

The K-theory of certainC∗-algebras endowed with gauge actions

“…In this paper we aim to compute the K-theory of two classes of generalized Cuntz-Krieger algebras: the Toeplitz algebras of finitely aligned higher rank graphs by Raeburn, Sims and Yeend [15], and E-mail address: bernhardburgstaller@yahoo.de. 1 higher rank Exel-Laca algebras [4] by the author under a condition called (II). More precisely we will show the following two theorems.…”

“…Suppose that (A, F, I) are the generators and relations generating a higher rank Exel-Laca algebra O A,F,I as described in [4]. We will assume that the partition V = {A 1 , .…”

“…. , A d } of A stated in Definition 2.2 of [4] is finite, A is non-degenerate in F/I, and F/I is non-degenerate in O A,F,I , i.e. we will regard A ⊆ F/I ⊆ F/I = O A,F,I , see also [6] for more on this.…”