Geodesic
COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS
Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 69-84

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DOI

In this paper, we introduce the notion of complex product structures on hom-Lie algebras and show that a hom-Lie algebra carrying a complex product structure is a double hom-Lie algebra and it is also endowed with a hom-left symmetric product. Moreover, we show that a complex product structure on a hom-Lie algebra determines uniquely a left symmetric product such that the complex and the product structures are invariant with respect to it. Finally, we introduce the notion of hyper-para-Kähler hom-Lie algebras and we present an example of hyper-para-Kähler hom-Lie algebras.
DOI : 10.1017/S001708951800006X
Mots-clés : 53C15, 53C25, 53D05 
NOURMOHAMMADIFAR, L.; PEYGHAN, E. COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS. Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 69-84. doi: 10.1017/S001708951800006X
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     title = {COMPLEX {PRODUCT} {STRUCTURES} {ON} {HOM-LIE} {ALGEBRAS}},
     journal = {Glasgow mathematical journal},
     pages = {69--84},
     year = {2019},
     volume = {61},
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     doi = {10.1017/S001708951800006X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708951800006X/}
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