On the representability of actions of Leibniz algebras and Poisson algebras

DOI10.1017/S0013091523000548arXiv2302.05175OpenAlexW4388879995MaRDI QIDQ6180586

Manuel Mancini, Giuseppe Metere, Alan S. Cigoli

Publication date: 22 December 2023

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.05175

zbMATH Keywords

associative algebraPoisson algebraLeibniz algebrasplit extensionaction representable category

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Poisson algebras (17B63) Derivations, actions of Lie algebras (16W25) Leibniz algebras (17A32) Automorphisms, derivations, other operators (nonassociative rings and algebras) (17A36) Protomodular categories, semi-abelian categories, Mal'tsev categories (18E13)

Cites Work

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• Action accessibility via centralizers
• Extensions and obstructions for rings
• A noncommutative version of Lie algebras: Leibniz algebras
• Cohomologically trivial internal categories in categories of groups with operations
• Universal strict general actors and actors in categories of interest
• Obstruction theory in action accessible categories
• Obstruction theory in algebraic categories. I
• Algebras with representable representations
• Central extensions of associative algebras and weakly action representable categories
• Semi-abelian categories

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