Hom-Lie quadratic and Pinczon Algebras |
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| Authors: | Didier Arnal Wissem Bakbrahem Ridha Chatbouri |
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| Institution: | 1. Institute of Mathematics of Burgundy, UMR CNRS, University of Burgundy, Faculty of Sciences and Technology, Dijon Cedex, Francedidier.arnal@u-bourgogne.fr;3. Mathematical Physics, Special Functions and Applications, High School of Sciences and Technology of Hammam Sousse, University of Sousse, Hammam Sousse, Tunisia |
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| Abstract: | Presenting the structure equation of a hom-Lie algebra 𝔤, as the vanishing of the self commutator of a coderivation of some associative comultiplication, we define up to homotopy hom-Lie algebras, which yields the general hom-Lie algebra cohomology with value in a module. If the hom-Lie algebra is quadratic, using the Pinczon bracket on skew symmetric multilinear forms on 𝔤, we express this theory in the space of forms. If the hom-Lie algebra is symmetric, it is possible to associate to each module a quadratic hom-Lie algebra and describe the cohomology with value in the module. |
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| Keywords: | Cohomology hom-Lie algebras quadratic algebras up to homotopy algebras |
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