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arXiv · 1707.07948

Cohomology characterizations of non-abelian extensions of Hom-Lie algebras

Lina Song·Rong Tang
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Abstract

In this paper, first we show that under the assumption of the center of h being zero, diagonal non-abelian extensions of a regular Hom-Lie algebra g by a regular Hom-Lie algebra h are in one-to-one correspondence with Hom-Lie algebra morphisms from g to Out(h). Then for a general Hom-Lie algebra morphism from g to Out(h), we construct a cohomology class as the obstruction of existence of a non-abelian extension that induce the given Hom-Lie algebra morphism.

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Lina Song, Rong Tang. 2017-07-25. Cohomology characterizations of non-abelian extensions of Hom-Lie algebras. https://arxiv.org/abs/1707.07948

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