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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-JĆ¼rgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


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Extensions of hom-Lie color algebras

Abdoreza Armakan / Sergei SilvestrovORCID iD: https://orcid.org/0000-0003-4554-6528 / Mohammad Reza Farhangdoost
Published Online: 2019-07-12 | DOI:Ā https://doi.org/10.1515/gmj-2019-2033

Abstract

In this paper, we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie color algebra š”¤ by another hom-Lie color algebra š”„ and discuss the case where š”„ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i.e., we show that in order to have an extendible hom-Lie color algebra, there should exist a trivial member of the third cohomology.

Keywords: Hom-Lie color algebras; cohomology of hom-Lie color algebras; extensions of hom-Lie color algebras

MSC 2010: 17B56; 17B75; 17B40

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About the article

Received: 2017-05-25

Accepted: 2018-09-04

Published Online: 2019-07-12


Funding Source: Shiraz University

Award identifier / Grant number: 92grd1m82582

The research in this paper has been supported by grant no. 92grd1m82582 of Shiraz University, Shiraz, Iran.


Citation Information: Georgian Mathematical Journal, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI:Ā https://doi.org/10.1515/gmj-2019-2033.

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