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Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras
Version 1
: Received: 26 April 2024 / Approved: 26 April 2024 / Online: 28 April 2024 (03:02:21 CEST)
A peer-reviewed article of this Preprint also exists.
Zhu, F.; You, T.; Teng, W. Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules. Axioms 2024, 13, 380. Zhu, F.; You, T.; Teng, W. Abelian Extensions of Modified λ-Differential Left-Symmetric Algebras and Crossed Modules. Axioms 2024, 13, 380.
Abstract
In this paper, we define the cohomology of a modified $\lambda$-differential left-symmetric algebra with coefficients in a suitable representation. We also introduce the notion of modified $\lambda$-differential left-symmetric 2-algebra.
We classify linear deformations and abelian extensions of modified $\lambda$-differential left-symmetric algebras using the second cohomology group and classify skeletal modified $\lambda$-differential left-symmetric 2-algebra using the third cohomology group as our propose cohomology applications.
Moreover, we prove that strict modified $\lambda$-differential left-symmetric 2-algebras are equivalent to crossed modules of modified $\lambda$-differential left-symmetric algebras.
Keywords
left-symmetric algebras; modified λ-differential operator; cohomology; deformation; abelian extension; crossed module
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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