Abstract
We study the structure of simple multiplicative Hom-Jordan algebras. We discuss equivalent conditions for multiplicative Hom-Jordan algebras to be solvable, simple, and semi-simple. Moreover, we give a theorem on the classification of simple multiplicative Hom-Jordan algebras and obtain some propositions about bimodules of multiplicative Hom-Jordan algebras.
Highlights
Algebras where the identities defining the structure are twisted by a homomorphism are called Hom-algebras
The theory of Hom-algebras started from Hom-Lie algebras introduced and discussed in [6, 10, 11, 12]
In [2], Ashihara gave a counterexample to the following assertion: If R is a subalgebra of the Griess algebra, the weight two space of the vertex operator subalgebra VOA(R) generated by R coincides with R by using a vertex operator algebra associated with the simple Jordan algebra of type D
Summary
Algebras where the identities defining the structure are twisted by a homomorphism are called Hom-algebras. Han gave a classification theorem about simple multiplicative Hom-Lie algebras. In [1], Agrebaoui, Benali, and Makhlouf studied representations of simple Hom-Lie algebras and gave some propositions about them. Some propositions about bimodules of simple Hom-Jordan algebras are obtained as an application of Theorem 5.5
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