Axioms (Jun 2024)
Abelian Extensions of Modified <i>λ</i>-Differential Left-Symmetric Algebras and Crossed Modules
Abstract
In this paper, we define a cohomology theory of a modified λ-differential left-symmetric algebra. Moreover, we introduce the notion of modified λ-differential left-symmetric 2-algebras, which is the categorization of a modified λ-differential left-symmetric algebra. As applications of cohomology, we classify linear deformations and abelian extensions of modified λ-differential left-symmetric algebras using the second cohomology group and classify skeletal modified λ-differential left-symmetric 2-algebra using the third cohomology group. Finally, we show that strict modified λ-differential left-symmetric 2-algebras are equivalent to crossed modules of modified λ-differential left-symmetric algebras.
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