Cosymplectic Jacobi-Jordan Algebras
S. El bourkadi, M. W. Mansouri

TL;DR
This paper introduces cosymplectic structures on Jacobi-Jordan algebras, explores their relation to symplectic counterparts, and provides a classification in dimension five, highlighting their algebraic properties and extension methods.
Contribution
It defines cosymplectic Jacobi-Jordan algebras, studies their properties, and classifies all such algebras in five dimensions for the first time.
Findings
Cosymplectic Jacobi-Jordan algebras support a right-skew-symmetric product.
A complete classification of five-dimensional cosymplectic Jacobi-Jordan algebras is provided.
Double extension constructions are used to analyze these algebras.
Abstract
We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that they support a right-skew-symmetric product. We also study the double extension constructions of cosymplectic Jacobi-Jordan algebras and give a complete classification in dimension five.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Operator Algebra Research
