On the combinatorial rank of quantum groups of type F4

In this paper, we calculate the combinatorial rank of the positive part Formula: see text of the multiparameter version of the small Lusztig quantum group, where Formula: see text is a simple Lie algebra of type Formula: see text. For this purpose, we also present the basis and relations of the quantum algebra, calculate the coproduct of its PBW-generators and determine all skew-primitive elements of this quantum group. In conclusion, we obtain that the combinatorial rank of Formula: see text is 4.