Statistical $\rho$-commutative algebras

Abstract

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

Keywords

• statistical structure
• Codazzi-couple
• Kähle structure
• Para-Kähler structure
• connection
• holomorphic statistical structure

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