Zhu, F.; You, T.; Teng, W. Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras. Preprints2024, 2024041750. https://doi.org/10.20944/preprints202404.1750.v1
APA Style
Zhu, F., You, T., & Teng, W. (2024). Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras. Preprints. https://doi.org/10.20944/preprints202404.1750.v1
Chicago/Turabian Style
Zhu, F., Taijie You and Wen Teng. 2024 "Abelian Extensions and Crossed Modules of Modified λ-Differential Left-Symmetric Algebras" Preprints. https://doi.org/10.20944/preprints202404.1750.v1
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.
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
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