Noncommutative Cartan $\mathrm {C}^*$-subalgebras
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- by Bartosz Kosma Kwaśniewski and Ralf Meyer PDF
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Abstract:
We characterise Exel’s noncommutative Cartan subalgebras in several ways using uniqueness of conditional expectations, relative commutants, or purely outer inverse semigroup actions. We describe in which sense the crossed product decomposition for a noncommutative Cartan subalgebra is unique. We relate the property of being a noncommutative Cartan subalgebra to aperiodic inclusions and effectivity of dual groupoids. In particular, we extend Renault’s characterisation of commutative Cartan subalgebras.References
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Additional Information
- Bartosz Kosma Kwaśniewski
- Affiliation: Department of Mathematics, University of Białystok, ul. K. Ciołkowskiego 1M, 15-245 Białystok, Poland
- ORCID: 0000-0002-5173-0519
- Email: bartoszk@math.uwb.edu.pl
- Ralf Meyer
- Affiliation: Mathematisches Institut, Georg-August-Universität Göttingen, Bunsenstraße 3–5, 37073 Göttingen, Germany
- MR Author ID: 624320
- ORCID: 0000-0001-9584-8028
- Email: rmeyer2@uni-goettingen.de
- Received by editor(s): August 21, 2019
- Received by editor(s) in revised form: March 31, 2020
- Published electronically: September 29, 2020
- Additional Notes: The first-named author was partially supported by the National Science Center (NCN), Poland, grant no. 2019/35/B/ST1/02684
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 8697-8724
- MSC (2010): Primary 46L55, 20M18, 22A22
- DOI: https://doi.org/10.1090/tran/8174
- MathSciNet review: 4177273