
Journal of Lie Theory 32 (2022), No. 4, 9971006 Copyright Heldermann Verlag 2022 On Extensions of Nilpotent Leibniz and Diassociative Algebras Erik Mainellis Dept. of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, U.S.A. mainel1@stolaf.edu [Abstractpdf] 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. Keywords: Nilpotent extensions, Leibniz algebras, diassociative, dendriform, Zinbiel. MSC: 17A30, 17A01, 17A32. [ Fulltextpdf (111 KB)] for subscribers only. 