Splitting of operations for alternative and Malcev structures

2013/12/19 by Sara Madariaga, Madariaga, Sara
Mathematics · #17-08 #17A30 #17A50 #17C99 #17D #17D05 #17D10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1312.5710

openalex publication_date 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we define pre-Malcev algebras and alternative quadri-algebras and prove that they generalize pre-Lie algebras and quadri-algebras respectively to the alternative setting. Constructions in terms bimodules, splitting of operations, and Rota-Baxter operators are discussed.

Citations

• Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
• Universal enveloping algebras of Leibniz algebras and (co)homology

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• BiHom-pre-alternative algebras and BiHom-alternative quadri-algebras
• Extended (tri)dendriform algebras, pre-Lie algebras and post-Lie algebras as companion structures of extended Rota-Baxter algebras
• Malcev Yang-Baxter equation, weighted O-operators on Malcev algebras and post-Malcev algebras
• Decompositions of algebras and post-associative algebra structures
• On the Lie algebra of a Malcev algebra