On Homogeneous Weighted Algebras

Abstract

We extend the concept of the “join” to the case of infinitely many weighted algebras. We study the problem of its uniqueness (up to weighted isomorphism) which gives rise to a natural notion of homogeneous weighted algebras. We show that several classes of weighted algebras coming from genetics are homogeneous and that homogeneity is preserved by duplication. Finally, we examine some well-known weighted algebras satisfying identities, as Bernstein, train, and evolution algebras.

Key Words:

• Bernstein algebras
• Evolution algebras
• Homogeneous weighted algebras
• The duplicate
• The join
• Train algebras
• Weighted algebras

AMS Classification:

• 17D92

ACKNOWLEDGMENT

We would like to thank the referee for his valuable comments and suggestions that improved the presentation of this article.

Notes

Communicated by I. P. Shestakov.