The isomorphism problem for tensor algebras of multivariable dynamical systems
Faculty Advisor
Date
2022
Keywords
isomorphism, tensor algebras
Abstract (summary)
We resolve the isomorphism problem for tensor algebras of unital multivariable dynamical systems. Specifically, we show that unitary equivalence after a conjugation for multivariable dynamical systems is a complete invariant for complete isometric isomorphisms between their tensor algebras. In particular, this settles a conjecture of Davidson and Kakariadis, Inter. Math. Res. Not. 2014 (2014), 1289–1311 relating to work of Arveson, Acta Math. 118 (1967), 95–109 from the 1960s, and extends related work of Kakariadis and Katsoulis, J. Noncommut. Geom. 8 (2014), 771–787.
Publication Information
Katsoulis, E., & Ramsey, C. (2022). The isomorphism problem for tensor algebras of multivariable dynamical systems. Forum of Mathematics, Sigma, 10, E81. https://doi.org/10.1017/fms.2022.73
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