## Isomorphisms of tensor algebras arising from weighted partial systems

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## Abstract:

We continue the study of isomorphisms of tensor algebras associated to $C^*$-correspondences in the sense of Muhly and Solel. Inspired by recent work of Davidson, Ramsey, and Shalit, we solve isomorphism problems for tensor algebras arising from weighted partial dynamical systems. We provide complete bounded / isometric classification results for tensor algebras arising from weighted partial systems, both in terms of the $C^*$-correspondences associated to them and in terms of the original dynamics. We use this to show that the isometric isomorphism and algebraic / bounded isomorphism problems are two distinct problems that require separate criteria to be solved. Our methods yield alternative proofs to classification results for Peters’ semi-crossed product due to Davidson and Katsoulis and for multiplicity-free graph tensor algebras due to Katsoulis, Kribs, and Solel.## References

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## Additional Information

**Adam Dor-On**- Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada
- Address at time of publication: Department of Mathematics, Technion - Israel institute of Technology, Haifa, 3200003, Israel
- Email: adoron@uwaterloo.ca
- Received by editor(s): July 29, 2015
- Received by editor(s) in revised form: August 11, 2016
- Published electronically: January 18, 2018
- Additional Notes: The author was partially supported by an Ontario Trillium Scholarship
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**370**(2018), 3507-3549 - MSC (2010): Primary 47L30, 46K50, 46H20; Secondary 46L08, 37A30
- DOI: https://doi.org/10.1090/tran/7045
- MathSciNet review: 3766857