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Articles 1 - 2 of 2
Full-Text Articles in Social and Behavioral Sciences
The Extension Class And Kms States For Cuntz-Pimsner Algebras Of Some Bi-Hilbertian Bimodules, Adam C. Rennie, David I. Robertson, Aidan Sims
The Extension Class And Kms States For Cuntz-Pimsner Algebras Of Some Bi-Hilbertian Bimodules, Adam C. Rennie, David I. Robertson, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
For bi-Hilbertian A-bimodules, in the sense of Kajiwara-Pinzari-Watatani, we construct a Kasparov module representing the extension class defining the Cuntz-Pimsner algebra. The construction utilises a singular expectation which is defined using the C*-module version of the Jones index for bi-Hilbertian bimodules. The Jones index data also determines a novel quasi-free dynamics and KMS states on these Cuntz-Pimsner algebras.
Equivalence And Stable Isomorphism Of Groupoids, And Diagonal-Preserving Stable Isomorphisms Of Graph C*-Algebras And Leavitt Path Algebras, Toke Meier Carlsen, Efren Ruiz, Aidan Sims
Equivalence And Stable Isomorphism Of Groupoids, And Diagonal-Preserving Stable Isomorphisms Of Graph C*-Algebras And Leavitt Path Algebras, Toke Meier Carlsen, Efren Ruiz, Aidan Sims
Faculty of Engineering and Information Sciences - Papers: Part A
We prove that ample groupoids with σ-compact unit spaces are equivalent if and only if they are stably isomorphic in an appropriate sense, and relate this to Matui's notion of Kakutani equivalence. We use this result to show that diagonal-preserving stable isomorphisms of graph C*-algebras or Leavitt path algebras give rise to isomorphisms of the groupoids of the associated stabilised graphs. We deduce that the Leavitt path algebras LZ(E2) and LZ(E2-) are not stably *-isomorphic.