Non-finitely Presented Lie Algebras of Type FP₂

2026/08/02 by Mark Shusterman
Mathematics · #math.RA #math.GR #msc:17B55 #msc:17B60 #msc:20J05 #msc:16S15 #msc:16S34

paper · pdf

arxiv created 2026/08/02 · arxiv updated 2026/08/04

Abstract

Building on work of Kassel--Loday and Zelmanov--Zhang, we show that a Steinberg Lie algebra of the complex group algebra of a (suitable) Bestvina--Brady group is of type FP₂ and is not finitely presented. This also allows us to answer the (homological) 0-1-2 question for Lie algebras.

Citations

• Virtual Surjection and the n-(n+1)-(n+2) Theorem for Discrete Groups
• Finite Presentation
• Subdirect sums of Lie algebras
• Graded Lie algebras of type FP