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arXiv · 2105.13969

Extensions of Nilpotent Algebras

Erik Mainellis
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Abstract

Given a pair of nilpotent Lie algebras $A$ and $B$, an extension $0\xrightarrow{} A\xrightarrow{} L\xrightarrow{} B\xrightarrow{} 0$ is not necessarily nilpotent. However, if $L_1$ and $L_2$ are extensions which correspond to lifts of a map $\Phi:B\xrightarrow{} \text{Out}(A)$, 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 the algebras of Loday. As an important consequence, we thereby gain its associative analogue as a special case of diassociative algebras.

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Erik Mainellis. 2021-05-28. Extensions of Nilpotent Algebras. https://arxiv.org/abs/2105.13969

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