Compatible anti-pre-Lie algebras
Zafar Normatov
TL;DR
This paper introduces compatible anti-pre-Lie algebras, explores their connections with related algebraic structures, and classifies 2-dimensional cases, advancing understanding of these algebraic systems.
Contribution
It defines compatible anti-pre-Lie algebras, investigates their relationships with anti-$ O$-operators and cocycles, and classifies low-dimensional instances.
Findings
Established the notion of compatible anti-pre-Lie algebras.
Connected compatible anti-pre-Lie algebras with anti-$ O$-operators and cocycles.
Classified all 2-dimensional compatible anti-pre-Lie algebras.
Abstract
In this paper, we introduce the notion of compatible anti-pre-Lie algebras and study relationship between them and the related structures such as anti--operators, commutative -cocycles on compatible Lie algebras. Moreover, we give the classification of -dimensional compatible anti-pre-Lie algebras from the classification of anti-pre-Lie algebras of the same dimension.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Algebra and Logic