Bass-Serre theory for Lie algebras: A homological approach

Autor(es)

Kochloukova, D. H. ^[1] ; Martinez-Perez, C. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil

^[2] Univ Zaragoza, Dept Matemat, Zaragoza 50009 - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Algebra; v. 585, p. 143-175, NOV 1 2021.
• Citações Web of Science: 0

Resumo

We develop a version of 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. (C) 2021 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático