Graded Lie algebras of type FP

2013/05/27 by Thomas Weigel, Weigel, Thomas · 2 citations
Mathematics · Physics and Astronomy · #17B70 16P90 16S37 17B60 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA) #math.RA #msc:16P90 #msc:16S37 #msc:17B60 #msc:17B70

paper · pdf · doi:10.48550/arxiv.1305.6118

arxiv created 2013/05/27 · openalex publication_date 2013/05/27 · arxiv updated 2013/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It will be shown that every N-graded Lie algebra generated in degree 1 of type FP with entropy less or equal to 1 must be finite-dimensional (cf. Thm. A). As a consequence every Koszul Lie algebra with entropy less or equal to 1 must be abelian (cf. Cor. C). These results are obtained from a generalized Witt formula (cf. Thm. D) for N-graded Lie algebras of type FP and the analysis of necklace polynomials at roots of unity.

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