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COMPLEX PRODUCT STRUCTURES ON HOM-LIE ALGEBRAS

Published online by Cambridge University Press:  12 March 2018

L. NOURMOHAMMADIFAR  and
E. PEYGHAN
L. NOURMOHAMMADIFAR
Affiliation:
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran e-mails: l-nourmohammadifar@phd.araku.ac.ir, e-peyghan@araku.ac.ir
E. PEYGHAN
Affiliation:
Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran e-mails: l-nourmohammadifar@phd.araku.ac.ir, e-peyghan@araku.ac.ir
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Abstract

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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.

Keywords

53C1553C2553D05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 69 - 84
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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