Hom-group graded algebras

Abstract

Structural mapping is an important method for studying algebraic structures. Hom-algebra and monoidal Hom-group are new structures produced by algebra and group structural mappings, respectively. These structures are important algebra and group generalizations and are closely related to them. Let (A,β) be a Hom-algebra and (G,α) a monoidal Hom-group. A structure of (A,β) graded by (G,α) is introduced; this structure is called Hom-group graded algebra. This study presents the definition of Hom-group graded algebra, provides some examples, and discusses its basic properties. Furthermore, a sufficient and necessary condition that makes (A,β) a strongly (G,α)-graded algebra is explored using a structure map β and unit 1_A. Finally, by using different maps, two sufficient and necessary conditions for a Hom-algebra to be a (G,α)-graded algebra are expressed in different ways.

Keywords

Hom-algebra / monoidal Hom-group / group graded / structural mapping

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Funding

The National Natural Science Foundation of China(12271089)

The National Natural Science Foundation of China(12471033)