Non-finitely Presented Lie Algebras of Type $FP_2$

Mark Shusterman

arXiv:2608.01339v1 Primary: math.RA Secondary: math.GR

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 $FP_2$ and is not finitely presented. This also allows us to answer the (homological) $0$-$1$-$2$ question for Lie algebras.

Disclosure

“’s research is co-funded by the European Union (ERC, Function Fields, 101161909). The author is grateful to Tal Cohen for the collaboration on n-n + 1-n + 2 questions in group theory which motivated this work. This note has been drafted by GPT 5.6 in response to a sequence of prompts by the author. References [BestvinaBrady97] M. Bestvina and N. Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997),”
PDF page 4

Classification: Drafting limited passages
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Verified: 2026-08-23T19:18:27.474089Z

Structural counts

Pages 4 pdf

Theorems 0 source

Lemmas 4 source

Propositions 0 source

Corollaries 0 source

Definitions 0 source

Displayed equations 16 source

Bibliography entries 13 source

Appendix pages 0 estimated

Count notes

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