Journal of Lie Theory

no. 4
On Extensions of Nilpotent Leibniz and Diassociative Algebras
Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 997-1006
Given a pair of nilpotent Lie algebras $A$ and $B$, an extension $0\rightarrow A\rightarrow L\rightarrow B\rightarrow 0$ is not necessarily nilpotent. However, if $L_1$ and $L_2$ are extensions which correspond to lifts of homomorphism $\Phi\colon B\rightarrow \text{Out}(A)$, it has been shown that $L_1$ is nilpotent if and only if $L_2$ is nilpotent. In the present paper, we prove analogues of this result for each algebra of Loday. As an important consequence, we thereby gain its associative analogue as a special case of diassociative algebras.
DOI: 10.5802/jolt.1262
Classification: 17A30, 17A01, 17A32
Keywords: Nilpotent extensions, Leibniz algebras, diassociative, dendriform, Zinbiel 
@article{JOLT_2022_32_4_a4,
     author = {E. Mainellis},
     title = {On {Extensions} of {Nilpotent} {Leibniz} and {Diassociative} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {997--1006},
     year = {2022},
     volume = {32},
     number = {4},
     doi = {10.5802/jolt.1262},
     zbl = {1521.17004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1262/}
}
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E. Mainellis. On Extensions of Nilpotent Leibniz and Diassociative Algebras. Journal of Lie Theory, Volume 32 (2022) no. 4, pp. 997-1006. doi: 10.5802/jolt.1262

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