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## The structure of the algebra of weak Jacobi forms for the root system $F_4$

We prove the polynomiality of the bigraded ring J_{*,*}^{w, O}(F_4) of weak Jacobi forms for the root system F_4 which are invariant with respect to the corresponding Weyl group. This work is a continuation of the joint article with V.A. Gritsenko, where the structure of algebras of the weak Jacobi forms related to the root systems of Dn type for 2\le n\le 8 was studied.