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Rehren proved that a primitive 2-generated axial algebra of Monster type$(\alpha,\beta)$ has dimension at most eight if$\alpha\notin\{2\beta,4\beta\}$. In this note we construct aninfinite-dimensional 2-generated primitive axial algebra of Monster type$(2,\frac{1}{2})$ over an arbitrary field $F$ with $char(F)\neq 2,3$. Thisshows that the second special case, $\alpha=4\beta$, is a true exception toRehren's bound.

An infinite-dimensional 2-generated primitive axial algebra of Monster type