On the definition of quasi-Jordan algebra

Details On the definition of quasi-Jordan algebra On the definition of quasi-Jordan algebra

2010-08-11

arxiv.org/abs/1008.2009v1

Mathematics

Rings and Algebras

8 pages, 5 tables

Scientific paper

Velasquez and Felipe recently introduced quasi-Jordan algebras based on the product $a \triangleleft b = \tfrac12 ( a \dashv b + b \vdash a )$ in an associative dialgebra with operations $\dashv$ and $\vdash$. We determine the polynomial identities of degree $\le 4$ satisfied by this product. In addition to right commutativity and the right quasi-Jordan identity, we obtain a new associator-derivation identity.

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