HOM-ALTERNATIVE ALGEBRAS AND HOM-JORDAN ALGEBRAS
By Abdenacer Makhlouf. 2009
107 citations recorded by the source corpus.
The main feature of Hom-algebras is that the identities deflning the structures are twisted by homomorphisms. The purpose of this paper is to introduce Hom-alternative algebras and Hom-Jordan algebras. We discuss some of their properties and provide construction procedures using ordinary alternative algebras or Jordan algebras. Also, we show that a plus algebra of Hom-associative algebra leads to Hom-Jordan algebra.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/636f0e72692c30e92f14fb21431eb298f272edeb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- Abdenacer Makhlouf
- Donald Yau
- Aron Gohr
- Sergei Silvestrov
- Yael Fregier
- Florin Panaite
- F. Ammar
- Y. Sheng
In Computational Theory and Mathematics
In Geometry and Topology
- Abdenacer Makhlouf
- Donald Yau
- Aron Gohr
- Sergei Silvestrov
- Yael Fregier
- Florin Panaite
- F. Ammar
- Y. Sheng
Citations in the corpus
- Paradigm of Nonassociative Hom-algebras and Hom-superalgebras (2010, background): “In this section, we consider, following [31], a generalization of Jordan algebra by twisting the usual Jordan identity (x · y) · x(2) = x · (y · x(2)).”
- Hom-bialgebras and comodule Hom-algebras (2008, background): “23], number theory [12], the various versionsof the Yang-Baxter equations, braid group representations, and quantum groups [28] - [35]. Other papers concerning Hom-type structures are [2]- [7], [10], [17] - [21], and [24] - [27]. A fundamental property of Lie algebras is that they are related to ass”
- Unital algebras of Hom-associative type and surjective or injective twistings (2009, background): “Also, recently, Ataguema, Makhlouf, and Silvestrov introduced Hom-Nambu and Hom-Nambu-Lie algebras and n-ary versions of Hom-associative algebras in [2], and Makhlouf introduced Hom-Jordan algebras in [14].”