Derivation Hom-Lie 2-algebras and non-abelian extensions of regular Horn-Lie algebras

作者：Song, Lina^*; Tang, Rong

来源：Journal of Algebra and Its Applications, 2018, 17(5): 1850081.

DOI：10.1142/S0219498818500810

• Hom-Lie algebras
• derivations
• non-abelian extensions
• Hom-Lie 2-algebras

In this paper, we introduce the notion of a derivation of a regular Hom-Lie algebra and construct the corresponding strict Hom-Lie 2-algebra, which is called the derivation Hom-Lie 2-algebra. As applications, we study non-abelian extensions of regular Hom-Lie algebras. We show that isomorphism classes of 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 homotopy classes of morphisms from g to the derivation Hom-Lie 2-algebra DER(h).

• 出版日期2018-5
• 单位吉林大学