Abstract:It is shown that a JB-algebra which can be generated by the union of two of its associative Jordan subalgebras is a JC-algebra, hence special. A similar refinement of Macdonald's principle for JB-algebras is obtained. Moreover, we prove that the free unital JB-algebra generated by $n$ projections is a JC-algebra if and only if $n\in \{1,2,3\}$. Finally, we give an explicit description of the free unital JB-algebra generated by two projections paralleling the Raeburn-Sinclair theorem for C*-algebras.
| Subjects: | Operator Algebras (math.OA); Functional Analysis (math.FA) |
| Cite as: | arXiv:2605.24427 [math.OA] |
| (or arXiv:2605.24427v1 [math.OA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24427 arXiv-issued DOI via DataCite (pending registration) |
From: Mark Roelands [view email]
[v1]
Sat, 23 May 2026 06:42:39 UTC (54 KB)
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