Medial and isospectral algebras

Abstract

The purpose of this paper is to give a systematic study of two new classes of commutative nonassociative algebras, the so-called isospectral and medial algebras. An isospectral algebra A is a generic commutative nonassociative algebra whose idempotents have the same Peirce spectrum. A medial algebra is algebra with identity (xy)(zw) = (xz)(yw). We show that these two classes are essentially coincide. We also prove that any medial spectral algebra is isomorphic to a certain isotopic deformation of the commutative associative quotient algebra K[z]/(z n − 1).Medial magma, Isospectral algebras, Quasigroups, Idempotents, Peirce decomposition