Just-infinite Jordan Banach algebras
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914352378937344 |
|---|---|
| author | Zhelyabin, Victor Mamontov, Andrey |
| author_facet | Zhelyabin, Victor Mamontov, Andrey |
| contents | 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 $H(A_1,*)\unlhd J \subseteq H(A_2,*).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_22616 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Just-infinite Jordan Banach algebras Zhelyabin, Victor Mamontov, Andrey Rings and Algebras 46L05, 46H99, 46L70, 17C99, 17C65 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 $H(A_1,*)\unlhd J \subseteq H(A_2,*).$ |
| title | Just-infinite Jordan Banach algebras |
| topic | Rings and Algebras 46L05, 46H99, 46L70, 17C99, 17C65 |
| url | https://arxiv.org/abs/2602.22616 |