No dialgebra has Gelfand-Kirillov dimension strictly between 1 and 2.

The Gelfand-Kirillov dimension measures the asymptotic rate of growth of algebras. For every associative dialgebra D , the quotient A D := D / I d (S) , where I d (S) is the ideal of D generated by the set S := { x ⊢ y − x ⊣ y ∣ x , y ∈ D } , is called the associative algebra associated to D . We show that G K d i m (D) ≤ 2 G K d i m (A D). Moreover, we prove that no associative dialgebra has Gelfand-Kirillov dimension strictly between 1 and 2. [ABSTRACT FROM AUTHOR]