The quantum group Uq⁺(F₄) as a quadratic-linear algebra

Let Uq⁺(g) U q + ( g ) be the multiparameter quantum Borel algebra, where g g is a simple Lie algebra. The purpose of this paper is to prove that, in the case that g g is a simple Lie algebra of type F₄ F 4 , the algebra Uq⁺(g) U q + ( g ) can be constructed as a quadratic-linear algebra, but it is not a quadratic-linear Koszul algebra.