Jacobi-Jordan algebras
Dietrich Burde, Alice Fialowski
TL;DR
This paper investigates finite-dimensional commutative algebras satisfying the Jacobi identity, known as Jacobi-Jordan algebras, providing their properties and classifying them in dimensions less than 7 over certain fields.
Contribution
It offers a classification of Jacobi-Jordan algebras in dimensions under 7 over algebraically closed fields with characteristic not 2 or 3.
Findings
Classification of Jacobi-Jordan algebras for n<7
Properties of Jacobi-Jordan algebras described
Connection to Jordan algebras established
Abstract
We study finite-dimensional commutative algebras, which satisfy the Jacobi identity. Such algebras are Jordan algebras. We describe some of their properties and give a classification in dimensions over algebraically closed fields of characteristic not or .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Geometry