The isomorphism problem for tensor algebras of multivariable dynamical systems
Forum of Mathematics, Sigma, Tome 10 (2022)
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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.
@article{10_1017_fms_2022_73,
author = {Elias G. Katsoulis and Christopher Ramsey},
title = {The isomorphism problem for tensor algebras of multivariable dynamical systems},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {10},
year = {2022},
doi = {10.1017/fms.2022.73},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.73/}
}
TY - JOUR AU - Elias G. Katsoulis AU - Christopher Ramsey TI - The isomorphism problem for tensor algebras of multivariable dynamical systems JO - Forum of Mathematics, Sigma PY - 2022 VL - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.73/ DO - 10.1017/fms.2022.73 LA - en ID - 10_1017_fms_2022_73 ER -
%0 Journal Article %A Elias G. Katsoulis %A Christopher Ramsey %T The isomorphism problem for tensor algebras of multivariable dynamical systems %J Forum of Mathematics, Sigma %D 2022 %V 10 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2022.73/ %R 10.1017/fms.2022.73 %G en %F 10_1017_fms_2022_73
Elias G. Katsoulis; Christopher Ramsey. The isomorphism problem for tensor algebras of multivariable dynamical systems. Forum of Mathematics, Sigma, Tome 10 (2022). doi: 10.1017/fms.2022.73
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