Iterating the Pimsner construction

2007/07/11 by Valentin Deaconu, Deaconu, Valentin · 2 citations
Mathematics · #46L05 (Primary) #46L55 #46L80 (Secondary) #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.0707.1710

openalex publication_date 2007/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For A a C^*-algebra, E₁, E₂ two Hilbert bimodules over A, and a fixed isomorphism χ: E₁⊗_AE₂→ E₂⊗_AE₁, we consider the problem of computing the K-theory of the Cuntz-Pimsner algebra \mathcal O_E₂⊗_A\mathcal O_E1 obtained by extending the scalars and by iterating the Pimsner construction. The motivating examples are a commutative diagram of Douglas and Howe for the Toeplitz operators on the quarter plane, and the Toeplitz extensions associated by Pimsner and Voiculescu to compute the K-theory of a crossed product. The applications are for Hilbert bimodules arising from rank two graphs and from commuting endomorphisms of abelian C^*-algebras.

Citations

• Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras
• Partial-isometric crossed products by semigroups of endomorphisms
• C*-algebras of commuting endomorphisms

Cited by

• Reduced C^*-algebras of Product Systems -- an E₀-semigroup and a Groupoid perspective
• Lifting isomorphisms in K-theory through gradings of C^*-algebras

Related

• Cuntz-Pimsner C*-algebras and crossed products by Hilbert C*-bimodules
• The Toeplitz algebra of a Hilbert bimodule
• K-theory of C*-algebras arising from commuting Hilbert bimodules and invariant ideals
• Poincare duality for Cuntz-Pimsner algebras of bimodules
• C*-algebras associated to product systems of Hilbert bimodules