Just-infinite Jordan Banach algebras
Victor Zhelyabin, Andrey Mamontov

TL;DR
This paper introduces and studies the concept of just-infinite JB-algebras, exploring their structure, classification, and relation to just-infinite C*-algebras, revealing that they are either spin factors or related to specific subalgebras of C*-algebras.
Contribution
It defines just-infinite JB-algebras, analyzes their structure, and establishes their connection to just-infinite C*-algebras, providing a classification framework.
Findings
Any just-infinite JB-algebra is either an infinite-dimensional spin factor or related to subalgebras of a C*-algebra.
Established a correspondence between just-infinite C*-algebras and their Jordan algebras of self-adjoint elements.
Connected the properties of just-infinite JB-algebras to the structure of their parent C*-algebras.
Abstract
By analogy with the well-established notions of just-infinite groups and just-infinite algebras, in particular -algebras, we initiate a study of just-infinite -algebras, i.e. infinite dimensional -algebras for which all proper quotients are finite dimensional. We investigate the connections between a just-infinite -algebra and its Jordan algebra of self-adjoint elements. We also show that any just-infinite -algebra either is a infinite-dimensional spin factor or there exists a -algebra and just-infinite norm-closed real -subalgebras and of such that
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Taxonomy
TopicsAdvanced Operator Algebra Research · Advanced Banach Space Theory · Advanced Algebra and Logic
