On the Free Jordan Algebras
Iryna Kashuba, Olivier Mathieu
TL;DR
This paper proposes a conjecture regarding the dimensions and characters of homogeneous components in free Jordan algebras, supported by computational evidence and new theoretical results, including the cyclicity of the Jordan operad.
Contribution
It introduces a conjecture on free Jordan algebra structures and proves the cyclicity of the Jordan operad, advancing theoretical understanding.
Findings
Numerical evidence supporting the conjecture
Proof of the cyclicity of the Jordan operad
New theoretical results on free Jordan algebras
Abstract
A conjecture for the dimension and the character of the homogenous components of the free Jordan algebras is proposed. As a support of the conjecture, some numerical evidences are generated by a computer and some new theoretical results are proved. One of them is the cyclicity of the Jordan operad.
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