The inter-relationship between isomorphisms of commutative and isomorphisms of non-commutative \(\log\)-algebras

This paper establishes a necessary and sufficient condition for the coincidence of non-commutative \(\log\)-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of \(\log\)-algebras built on non-commutative von Neumann algebras...

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Bibliographic Details
Published in:arXiv.org 2024-08
Main Authors: Abdullaev, Rustam, Azizov, Azizkhon
Format: Article
Language:English
Subjects:
Isomorphism
Online Access:Get full text
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Summary:This paper establishes a necessary and sufficient condition for the coincidence of non-commutative \(\log\)-algebras constructed from different exact normal semifinite traces. Consequently, we provide a criterion for the isomorphism of \(\log\)-algebras built on non-commutative von Neumann algebras with different exact normal semifinite traces. Additionally, we demonstrate a connection between the isomorphism of non-commutative \(\log\)-algebras and the isomorphism of the corresponding \(\log\)-algebras constructed on the center of these von Neumann algebras. Furthermore, we present a necessary and sufficient condition for the isomorphism of \(\log\)-algebras derived from different von Neumann algebras of type \(I_n\).
ISSN:2331-8422