- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 2
- Statistical $\\rho$-commutative algebras
Statistical $\\rho$-commutative algebras
Authors : Zahra Bagheri, Esmaeil Peyghan
Pages : 340-355
Doi:10.15672/hujms.1105421
View : 9 | Download : 4
Publication Date : 2023-03-31
Article Type : Research
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