Generalized derivations of multiplicative \(n\)-ary \(\operatorname{Hom}\text{-}\Omega\) color algebras. (English) Zbl 1464.17007
Summary: We generalize the results of Leger and Luks, Zhang R. and Zhang Y.; Chen, Ma, Ni, Niu, Zhou and Fan; Kaygorodov and Popov about generalized derivations of color \(n\)-ary algebras to the case of \(n\)-ary \(\operatorname{Hom}\text{-}\Omega\) color algebras. Particularly, we prove some properties of generalized derivations of multiplicative \(n\)-ary \(\operatorname{Hom}\text{-}\Omega\) color algebras. Moreover, we prove that the quasiderivation algebra of any multiplicative \(n\)-ary \(\operatorname{Hom}\text{-}\Omega\) color algebra can be embedded into the derivation algebra of a larger multiplicative \(n\)-ary \(\operatorname{Hom}\text{-}\Omega\) color algebra.
MSC:
| 17A36 | Automorphisms, derivations, other operators (nonassociative rings and algebras) |
| 17A42 | Other \(n\)-ary compositions \((n \ge 3)\) |
| 17B61 | Hom-Lie and related algebras |
| 17D30 | (non-Lie) Hom algebras and topics |
Keywords:
generalized derivation; color algebra; Hom-algebra; Hom-Lie superalgebra; \(n\)-ary algebraReferences:
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