A uniqueness theorem for the Nica-Toeplitz algebra of a compactly\n aligned product system

2017/05/01 by James Fletcher, Fletcher, James
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Operator Algebra Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1705.00775

Abstract

Fowler introduced the notion of a product system: a collection of Hilbert\nbimodules \X= \\X_p:p\∈ P \ indexed by a\nsemigroup P, endowed with a multiplication implementing isomorphisms\n\X_p\⊗_A \X_q\≅ \X_pq. When P is\nquasi-lattice ordered, Fowler showed how to associate a C^*-algebra\n\NT_\X to \X, generated by a universal\nrepresentation satisfying some covariance condition. In this article we prove a\nuniqueness theorem for these so called Nica-Toeplitz algebras.\n

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