On special identities for dialgebras

Abstract

For every variety of algebras over a field, there is a natural definition of a corresponding variety of dialgebras (Loday-type algebras). In particular, Lie dialgebras are equivalent to Leibniz algebras. We use an approach based on the notion of an operad to study the problem of finding special identities for dialgebras. It is proved that all polylinear special identities for dialgebras can be obtained from special identities for corresponding algebras by means of a simple procedure. A particular case of this result confirms the conjecture by M. Bremner, R. Felipe, and J. Sanchez-Ortega, arXiv:1108.0586.

14 pages

References in corpus (3)

• Koszul duality for Operads
• Jordan Triple Disystems
• On the definition of quasi-Jordan algebra

Cited by in corpus (7)

• Jordan Trialgebras and Post-Jordan Algebras
• Transposed Poisson structures
• Special identities for the pre-Jordan product in the free dendriform algebra
• Replicating of binary operads, Koszul duality, Manin products and average operators
• Operads of decorated trees and their duals
• Matching Rota-Baxter algebras, matching dendriform algebras and matching pre-Lie algebras
• Veronese powers of operads and pure homotopy algebras