Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules

Autor:	Fuyang Zhu, Taijie You, Wen Teng
Jazyk:	angličtina
Rok vydání:	2024
Předmět:	left-symmetric algebra modified λ-differential operator cohomology deformation abelian extension crossed module Mathematics QA1-939
Zdroj:	Axioms, Vol 13, Iss 6, p 380 (2024)
Druh dokumentu:	article
ISSN:	2075-1680
DOI:	10.3390/axioms13060380
Popis:	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.
Databáze:	Directory of Open Access Journals
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