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

Rustam Abdullaev, Azizkhon Azizov
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Abstract

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 $I_n$.
交换代数的同构与非交换代数的同构之间的相互关系
本文为由不同的精确正态半有限迹所构造的非交换$\log$-gebras的共存建立了一个必要条件和充分条件。因此,我们为建立在具有不同精确正态半有限迹的非交换冯-诺依曼代数上的$\log$-代数的同构提供了一个标准。此外,我们证明了非交换 $\log$-gebras 的同构性与在这些 von Neumann 对象的中心上构造的相应 $\log$-gebras 的同构性之间的联系。此外,我们还提出了从 $I_n$ 类型的不同 von Neumann 对象衍生的 $\log$ 对象的同构性的必要和充分条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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