Statistical $\rho$-commutative algebras

In this article, we study Codazzi-couples of an arbitrary connection $\nabla$ with a nondegenerate 2-form $\omega$, isomorphism $L$ on the space derivation $\rho$-commutative algebra $A$, which important examples are almost complex and para-complex structures, metric $g$ that $(g, \omega,L)$ form compatible triple. We statistical structure algebras by classical manner Riemannian manifolds. Then recalling notions (para-)Kähler algebras, generalized notion Codazzi-(para-)Kähler as (or Fedosov) is at same time moreover define holomorphic algebras.