Contributions to the theory of \(C^*\)-correspondences with applications to multivariable dynamics (Q2844852)

The article under review is both motivated by and build on the work of \textit{K. R. Davidson} and \textit{J. Roydor} [Proc. Edinb. Math. Soc., II. Ser. 53, No. 2, 333--351 (2010; Zbl 1219.47143); corrigendum ibid. 54, No. 3, 643--644 (2011; Zbl 1226.47102)] and \textit{J. R. Peters} [Contemporary Mathematics 503, 197--215 (2009; Zbl 1194.46096)]. The central result of the paper under review is the result that the Cuntz-Pimsner \(C^{*}\)-algebra of an arbitrary multivariable system is Morita equivalent to the Cuntz-Pimsner of an injective one (Theorem 4.2) and, moreover, that it is a crossed product \(B \rtimes_{\beta} \mathbb{N}\) of a \(C^{*}\)-algebra \(B\) by an injective endomorphism \(\beta\) (Theorem 4.6).