An algebra with identities a(bc) = b(ac), (ab)c = (ac)b is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.
No takes yet. Share an insight, caveat, or question.
Dzhumadil’daev et al. (2018) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: