On \(\mathsf{Lie}\)-isoclinic extensions of Leibniz \(n\)-algebras (Q6572380)
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scientific article; zbMATH DE number 7881004
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(\mathsf{Lie}\)-isoclinic extensions of Leibniz \(n\)-algebras |
scientific article; zbMATH DE number 7881004 |
Statements
On \(\mathsf{Lie}\)-isoclinic extensions of Leibniz \(n\)-algebras (English)
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15 July 2024
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Isoclinism in groups was developed by \textit{P. Hall} [J. Reine Angew. Math. 182, 130--141 (1940; JFM 66.0081.01)] as a generalization of isomorphism. The concept was developed in Lie algebras by \textit{K. Moneyhun} [Algebras Groups Geom. 11, No. 1, 9--22 (1994; Zbl 0801.17005)]. Both concepts have attracted much interest in groups and classes of algebras. The present work considers Lie-isoconic extensions of Leibniz \(n\)-algebras. Several conditions showing that Lie-central extensions of Leibniz \(n\)-algebras are Lie-isoclinic are given. The Schur Lie-multiplier of Leibniz \(n\)-algebras is investigated. Connections between Lie-isoclinism and Lie-stem covers are studied.
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Leibniz \(n\)-algebra
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Lie-central extension
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Lie-isoclinism
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Schur Lie-multiplier
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