The universal associative enveloping algebra of a Lie–Jordan algebra with a unit

We describe the universal associative enveloping algebra of a Lie–Jordan algebra with a unit over a field of characteristic 0. We show that if L is a Lie–Jordan algebra with a unit e over a field FF of characteristic 0, then the (unital) universal associative envelope of L is isomorphic to F⋅1⊕L⊕eL,F·1⊕L⊕eL, where eL={ex|x∈L}.eL={ex|x∈L}. The center of the universal associative envelope is also described. We conclude the paper with some open problems for further research