Bass-Serre theory for Lie algebras: a homological approach

2021/01/05 by Kochloukova, Dessislava H., Martínez-Pérez, Conchita · 1 citation
#17B55 #20J05 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2101.01411

Abstract

We develop a version of the Bass-Serre theory for Lie algebras (over a field k) via a homological approach. We define the notion of fundamental Lie algebra of a graph of Lie algebras and show that this construction yields Mayer-Vietoris sequences. We extend some well known results in group theory to ℕ-graded Lie algebras: for example, we show that one relator ℕ-graded Lie algebras are iterated HNN extensions with free bases which can be used for cohomology computations and apply the Mayer-Vietoris sequence to give some results about coherence of Lie algebras.

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• Restricted graph Lie algebras in even characteristic

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