Statistical $\rho$-commutative algebras

Year 2023, Volume: 52 Issue: 2, 340 - 355, 31.03.2023

Zahra Bagheri Esmaeil Peyghan

https://doi.org/10.15672/hujms.1105421

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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