Compatible actions of Lie algebras |
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Authors: | Davide Di Micco |
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Affiliation: | 1. Dipartimento di matematica “Federigo Enriques”, Università degli Studi di Milano, Milano, Italydavide.dimicco@unimi.it |
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Abstract: | AbstractWe study compatible actions (introduced by Brown and Loday in their work on the non-abelian tensor product of groups) in the category of Lie algebras over a fixed ring. We describe the Peiffer product via a new diagrammatic approach, which specializes to the known definitions both in the case of groups and of Lie algebras. We then use this approach to transfer a result linking compatible actions and pairs of crossed modules over a common base object L from groups to Lie algebras. Finally, we show that the Peiffer product, naturally endowed with a crossed module structure, has the universal property of the coproduct in XModL(LieR). |
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Keywords: | Compatible actions crossed modules Lie algebras Peiffer product |
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