Geodesic
On Extensions of Nilpotent Leibniz and Diassociative Algebras
Erik Mainellis1
1Dept. of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, U.S.A.
Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 997-1006

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17A30, 17A01, 17A32
Mots-clés : Nilpotent extensions, Leibniz algebras, diassociative, dendriform, Zinbiel

Erik Mainellis  1

1 Dept. of Mathematics, Statistics and Computer Science, St. Olaf College, Northfield, U.S.A. 
Erik Mainellis. On Extensions of Nilpotent Leibniz and Diassociative Algebras. Journal of Lie Theory, Tome 32 (2022) no. 4, pp. 997-1006. http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a4/
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     title = {On {Extensions} of {Nilpotent} {Leibniz} and {Diassociative} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {997--1006},
     year = {2022},
     volume = {32},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2022_32_4_a4/}
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