Omni-Representations of Leibniz Algebras |
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| Affiliation: | 1.Department of Mathematics,Peking University,Beijing 100871,P.R.China;2.Department of Mathematics,Jilin University,Changchun 130012,P.R.China |
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| Abstract: | In this paper,first we introduce the notion of an omni-representation of a Leibniz algebra g on a vector space V as a Leibniz algebra homomor-phism from g to the omni-Lie algebra gl(V)⊕ V.Then we introduce the omni-cohomology theory associated to omni-representations and establish the re-lation between omni-cohomology groups and Loday-Pirashvili cohomology groups. |
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| Keywords: | Leibniz algebra omni-Lie algebra representation cohomology |
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