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- W2950397352 abstract "We prove that the celebrated It^{o}'s theorem for groups remains valid at the level of Leibniz algebras: if $mathfrak{g}$ is a Leibniz algebra such that $mathfrak{g} = A + B$, for two abelian subalgebras $A$ and $B$, then $mathfrak{g}$ is metabelian, i.e. $[ , [mathfrak{g}, , mathfrak{g}], , [ mathfrak{g}, , mathfrak{g} ] , ] = 0$. A structure type theorem for metabelian Leibniz/Lie algebras is proved. All metabelian Leibniz algebras having the derived algebra of dimension $1$ are described, classified and their automorphisms groups are explicitly determined as subgroups of a semidirect product of groups $P^* ltimes bigl(k^* times {rm Aut}_{k} (P) bigl)$ associated to any vector space $P$." @default.
- W2950397352 created "2019-06-27" @default.
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- W2950397352 date "2014-01-19" @default.
- W2950397352 modified "2023-10-14" @default.
- W2950397352 title "It^o's theorem and metabelian Leibniz algebras" @default.
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- W2950397352 doi "https://doi.org/10.48550/arxiv.1401.4675" @default.
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