Polynomial identities of bicommutative algebras, Lie and Jordan elements

2017/11/12 by Askar Dzhumadil’daev, A. S. Dzhumadil'daev, Dzhumadil'daev, A. S. +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1711.04300

14 pages

arxiv created 2017/11/12 · openalex publication_date 2017/11/12 · arxiv updated 2017/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An algebra with identities a(bc)=b(ac), (ab)c=(ac)b is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.

Citations

• Four dimensional Jordan algebras
• Varieties of bicommutative algebras

Cited by

• δ-Novikov and δ-Novikov--Poisson algebras

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