The Formanek-Procesi group with base a right-angled Artin group: Residual nilpotence and Lie algebra
V. Metaftsis, A.I. Papistas
TL;DR
This paper studies the Lie algebra structure of the Formanek-Procesi group with a right-angled Artin base, revealing its presentation and Magnus group property, advancing understanding of its algebraic properties.
Contribution
It provides a presentation of the Lie algebra of FP(H) and proves that FP(H) is a Magnus group, linking group presentation to Lie algebra structure.
Findings
Lie algebra of FP(H) has a presentation dictated by the group presentation
FP(H) is shown to be a Magnus group
Advances understanding of algebraic properties of FP(H)
Abstract
We investigate the Lie algebra of the Formanek-Procesi group FP(H) with base group H a right-angled Artin group. We show that the Lie algebra gr(FP(H)) has a presentation that is dictated by the group presentation. Moreover we show that FP(H) is a Magnus group.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models