Omni-representations of Leibniz algebras. (English) Zbl 07812205
Summary: 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 homomorphism from \(g\) to the omni-Lie algebra \(\mathfrak{gl} (V) \oplus V\). Then we introduce the omni-cohomology theory associated to omni-representations and establish the relation between omni-cohomology groups and Loday-Pirashvili cohomology groups.
MSC:
| 17B99 | Lie algebras and Lie superalgebras |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
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