Abstract
It is shown that the existence of nontrivial scalar Lie fields (i. e. fields whose commutator is linear in the field itself) is not precluded by algebraic consistency arguments. A partial characterization of the simplest algebraic Lie field structures is given. Several examples are presented, one of which may be represented by Hermitian operators in a Hilbert space having a unitary representation of the Poincaré group.
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