Tying up baric algebras

Given two baric algebras $(A_1,ω_1)$ and $(A_2,ω_2)$ we describe a way to define a new baric algebra structure over the vector space $A_1\oplus A_2$, which we shall denote $(A_1\bowtie A_2,ω_1\bowtieω_2)$. We present some easy properties of this construction and we show that in the commutative and unital case it preserves indecomposability. Algebras of the form $A_1\bowtie A_2$ in the associative, coutable-dimensional, zero-characteristic case are classified.

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