On the Definition of Quasi-Jordan Algebra

Abstract

Velásquez and Felipe recently introduced quasi-Jordan algebras based on the product in an associative dialgebra with operations ⊣ and ⊢. We determine the polynomial identities of degree ≤4 satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity.

Key Words:

• Associative dialgebras
• Computer algebra
• Polynomial identities
• Quasi-Jordan algebras

2000 Mathematics Subject Classification:

• Primary 17A30
• Secondary 17-04, 17A15, 17A32, 17A50, 17C05, 17C50

ACKNOWLEDGMENTS

I thank Raúl Felipe, Luiz Peresi, Alexandre Pozhidaev, and the referee for very helpful comments. This research was partially supported by NSERC, the Natural Sciences and Engineering Research Council of Canada.

Notes

Communicated by A. Elduque.