Mathematics – Rings and Algebras
Scientific paper
2008-10-17
Proc. London Math. Soc. (3) 103 (2011), no. 4, 601-653
Mathematics
Rings and Algebras
55 pages. Version 3 is a complete rewrite of version 2. In version 4 Def. 3.14, Def. 4.6, Def. 4.8 and Remark 4.9 have been ad
Scientific paper
10.1112/plms/pdq040
From a system consisting of a right non-degenerate ring $R$, a pair of $R$-bimodules $Q$ and $P$ and an $R$-bimodule homomorphism $\psi:P\otimes Q\longrightarrow R$ we construct a $\Z$-graded ring $\mathcal{T}_{(P,Q,\psi)}$ called the Toeplitz ring and (for certain systems) a $\Z$-graded quotient $\mathcal{O}_{(P,Q,\psi)}$ of $\mathcal{T}_{(P,Q,\psi)}$ called the Cuntz-Pimsner ring. These rings are the algebraic analogs of the Toeplitz $C^*$-algebra and the Cuntz-Pimsner $C^*$-algebra associated to a $C^*$-correspondence (also called a Hilbert bimodule). This new construction generalizes for example the algebraic crossed product by a single automorphism, corner skew Laurent polynomial ring by a single corner automorphism and Leavitt path algebras. We also describe the structure of the graded ideals of our graded rings in terms of pairs of ideals of the coefficient ring.
Carlsen Toke Meier
Ortega Eduard
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