On the Shirshov--Cohn theorem for JB-algebras
Operator Algebras
2026-05-26 v1 Functional Analysis
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 projections is a JC-algebra if and only if . Finally, we give an explicit description of the free unital JB-algebra generated by two projections paralleling the Raeburn-Sinclair theorem for C*-algebras.
Cite
@article{arxiv.2605.24427,
title = {On the Shirshov--Cohn theorem for JB-algebras},
author = {Mark Roelands and Samuel Tiersma},
journal= {arXiv preprint arXiv:2605.24427},
year = {2026}
}