Jacobi-Jordan algebras

2014/04/22 by Burde, Dietrich, Fialowski, Alice · 4 citations
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1404.5435

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 n<7 over algebraically closed fields of characteristic not 2 or 3.

Cited by

• Extensions of pseudo-euclidean mock-Lie superalgebras
• Representations of weighted Rota-Baxter Jacobi-Jordan algebras
• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
• Cohomologies and linear deformations of pre-Jacobi-Jordan algebras

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• Classifications of two-dimensional Jordan algebras over the algebraically closed fields and ℝ
• The Jacobian algebras
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• On a pre-Jacobi-Jordan algebra: relevant properties and double construction
• Nonassociative algebras of anti-biderivation-type