  This work addresses some relevant characteristics of associative algebras in
low dimensions. Especially, given 1 and 2 dimensional associative algebras, we
explicitly solve associative Yang-Baxter equations and use skew-symmetric
solutions to perform double constructions of Frobenius algebras. Besides, we
determine related compatible dendriform algebras and solutions of their $ D-
$equations. Finally, using symmetric solutions of the latter equations, we
proceed to double constructions of corresponding Connes cocycles.
