C*-crossed products and shift spaces

Details C*-crossed products and shift spaces C*-crossed products and shift spaces

2005-12-21

arxiv.org/abs/math/0512488v1

Expo. Math. 25 (2007), no. 4, 275-307.

Mathematics

Operator Algebras

29 pages

Scientific paper

10.1016/j.exmath.2007.02.004

In this article, we use Exel's construction to associate a C*-algebra to every shift space. We show that it has the C*-algebra defined in [Carlsen and Matsumoto: Some remarks on the C*-algebras associated with subshifts] as a quotient, and possesses properties indicating that it can be thought of as the universal C*-algebra associated to a shift space. We also consider its representations, relationship to other C*-algebras associated to shift spaces, show that it can be viewed as a generalization of the universal Cuntz-Krieger algebra, discuss uniqueness and a faithful representation, provide conditions for it being nuclear, for satisfying the UCT, for being simple, and for being purely infinite, show that the constructed algebras and thus their K-theory, $K_0$ and $K_1$, are conjugacy invariants of one-sided shift spaces, present formulas for those invariants, and also present a description of the structure of gauge invariant ideals.

Affiliated with

Also associated with

No associations

Rating

C*-crossed products and shift spaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with C*-crossed products and shift spaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and C*-crossed products and shift spaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422309