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arXiv · 2602.22616

Just-infinite Jordan Banach algebras

Victor Zhelyabin·Andrey Mamontov
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Abstract

By analogy with the well-established notions of just-infinite groups and just-infinite algebras, in particular $C^*$-algebras, we initiate a study of just-infinite $JB$-algebras, i.e. infinite dimensional $JB$-algebras for which all proper quotients are finite dimensional. We investigate the connections between a just-infinite $C^*$-algebra $A$ and its Jordan algebra $H(A,*)$ of self-adjoint elements. We also show that any just-infinite $JB$-algebra $J$ either is a infinite-dimensional spin factor or there exists a $C^*$-algebra $A$ and just-infinite norm-closed real $*$-subalgebras $A_1$ and $A_2$ of $A$ such that $H(A_1,*)\unlhd J \subseteq H(A_2,*).$

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Victor Zhelyabin, Andrey Mamontov. 2026-02-26. Just-infinite Jordan Banach algebras. https://arxiv.org/abs/2602.22616

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