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C\*-crossed Products and Shift Spaces by Toke Meier Carlsen; Sergei Silvestrov is a Mathematics article available to read on EtoBox.

What is C\*-crossed Products and Shift Spaces about?

We use Exel's C \* -crossed products associated to non-invertible dynamical systems to associate a C \* -algebra to arbitrary shift space. We show that this C \* -algebra is canonically isomorphic to the C \* -algebra associated to a shift space given by Carlsen [Cuntz-Pimsner C \* -algebras associated with subshifts, Internat. J. Math. ( 2004) 28, to appear, available at arXiv:math.OA/0505503], has the C \* -algebra defined by Carlsen and Matsumoto [Some remarks on the C \* -algebras associated with subshifts, Math. Scand. 95 (1) (2004) 145-160] 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 and its relationship to other C \* -algebras associated to shift spaces. We show that it can be viewed as a generalization of the universal Cuntz-Krieger algebra, discuss uniqueness and present a faithful representation, show that it is nuclear and satisfies the Universal Coefficient Theorem, provide conditions for it being simple and purely infinite, show that the constructed C \* -algebras and thus their K-theory, K 0 and K 1 , are conjugacy invariants of one-sided s

Who reads C\*-crossed Products and Shift Spaces?

Author

Toke Meier Carlsen; Sergei Silvestrov

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0723-0869)

Published

2007

Language

EN

Field

Mathematics (Physical Sciences)