Geodesic
Product structures and complex structures of Hom-Lie-Yamaguti algebras
Filomat, Tome 35 (2021) no. 15, p. 5115

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DOI

In this paper, we mainly discuss linear deformations of a Hom-Lie-Yamaguti algebra and introduce the notion of a Hom-Nijenhuis operator. We introduce the notion of a product structure on a Hom-Lie-Yamaguti algebra, which is a Hom-Nijenhuis operator E satisfying E 2 = Id. There is a product structure on an involutive Hom-Lie-Yamaguti algebra if and only if the Hom-Lie-Yamaguti algebra is the direct sum of two subalgebras (as vector spaces). At the same time, we also introduce the notion of a complex structure on a Hom-Lie-Yamaguti algebra. Finally, we add a compatibility condition between a product structure and a complex structure to introduce the notion of a complex product structure on an involutive Hom-Lie-Yamaguti algebra
DOI : 10.2298/FIL2115115D
Classification : 17B56
Keywords: Hom-Lie-Yamaguti algebra, Hom-Nijenhuis operator, product structure, complex structure, complex product structure 
Lihong Dong; Liuhui Ma. Product structures and complex structures of Hom-Lie-Yamaguti algebras. Filomat, Tome 35 (2021) no. 15, p. 5115 . doi: 10.2298/FIL2115115D
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     title = {Product structures and complex structures of {Hom-Lie-Yamaguti} algebras},
     journal = {Filomat},
     pages = {5115 },
     year = {2021},
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     doi = {10.2298/FIL2115115D},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2115115D/}
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