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2014 $L$-Modules, $L$-Comodules and Hom-Lie Quasi-Bialgebras
I. Bakayoko
Afr. Diaspora J. Math. (N.S.) 17(1): 49-64 (2014).

Abstract

In this paper, we discuss $A$-modules and $L$-modules (resp. $L$-comodules) for Hom-Lie algebras (resp. Hom-Lie coalgebras). We show that for a given Hom-associative algebra $A$ (resp. Hom-coassociative coalgebra), the $A$-module (resp. comodule) extends to $L(A)$-module (resp. comodule), where $L(A)$ is the associated Lie algebra (resp. Lie coalgebra), with the same structure map. We also prove that $L$-modules become $L_\alpha$-modules, where $L_\alpha$ is the Hom-Lie algebra obtained from the Lie algebra $L$ by stwisting the Lie bracket. Then we introduce Hom-Lie quasi-bialgebras and prove that a Lie quasi-bialgebra turns to a Hom-Lie quasi-bialgebra by stwisting the Lie quasi-bialgebra structure by an endomorphism. Moreover, we show that an exact Lie quasi-bialgebra extends to an exact Hom-Lie quasi-bialgebra.

Citation

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I. Bakayoko. "$L$-Modules, $L$-Comodules and Hom-Lie Quasi-Bialgebras." Afr. Diaspora J. Math. (N.S.) 17 (1) 49 - 64, 2014.

Information

Published: 2014
First available in Project Euclid: 20 October 2014

zbMATH: 1321.16023
MathSciNet: MR3270012

Subjects:
Primary: 16D10, 16T15, 17B62

Rights: Copyright © 2014 Mathematical Research Publishers

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