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- W2131291647 abstract "We introduce and provide a classification theorem for the class of Heisenberg-Fock Leibniz algebras. This category of algebras is formed by those Leibniz algebras $L$ whose corresponding Lie algebras are Heisenberg algebras $H_n$ and whose ${H_n}$-modules $I$, where $I$ denotes the ideal generated by the squares of elements of $L$, are isomorphic to Fock modules. We also consider the three-dimensional Heisenberg algebra $H_3$ and study three classes of Leibniz algebras with $H_3$ as corresponding Lie algebra, by taking certain generalizations of the Fock module. Moreover, we describe the class of Leibniz algebras with $H_n$ as corresponding Lie algebra and such that the action $I times H_n to I$ gives rise to a minimal faithful representation of $H_n$. The classification of this family of Leibniz algebras for the case of $n=3$ is given." @default.
- W2131291647 created "2016-06-24" @default.
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- W2131291647 date "2014-11-14" @default.
- W2131291647 modified "2023-10-18" @default.
- W2131291647 title "Leibniz algebras of Heisenberg type" @default.
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- W2131291647 doi "https://doi.org/10.48550/arxiv.1411.3861" @default.
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