Splitting of operations for alternative and Malcev structures

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.

16 pages, 2 figures

References in corpus (4)

• Loday-type Algebras and the Rota-Baxter Relation
• Some results on L-dendriform algebras
• On Products and Duality of Binary, Quadratic, Regular Operads
• Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions