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arXiv · 2609.05051

Extending Structures for $n$-Lie Algebras

Tao Zhang
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Abstract

We revist the cohomology theory of $n$-Lie algebras in three different ways: cohomology theory of Leibniz algebras, infinitesimal deformation and abelian extension. In the main part of this paper, we study extending structures for $n$-Lie algebras. A necessary and sufficient unified-product criterion is obtained. The case of crossed products, sparse non-abelian extensions, matched pairs are studied as special cases. We also investigate the factorizations, deformation maps, and complements problem for $n$-Lie algebras. An appendix removes the general non-reduced unified product with all intermediate mixed mcomponents.

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Tao Zhang. 2026-09-04. Extending Structures for $n$-Lie Algebras. https://arxiv.org/abs/2609.05051

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