It will be shown that every ℕ-graded Lie algebra generated in degree 1 of type FP with entropy less than or equal to 1 must be finite-dimensional (cf. Thm. A). As a consequence every Koszul Lie algebra with entropy less than 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.
Weigel, T. (2015). Graded Lie algebras of type FP. ISRAEL JOURNAL OF MATHEMATICS, 205(1), 185-209 [10.1007/s11856-014-1131-y].
Graded Lie algebras of type FP
WEIGEL, THOMAS STEFAN
2015
Abstract
It will be shown that every ℕ-graded Lie algebra generated in degree 1 of type FP with entropy less than or equal to 1 must be finite-dimensional (cf. Thm. A). As a consequence every Koszul Lie algebra with entropy less than 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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
arxivversion.pdf
accesso aperto
Descrizione: versione sul arxiv
Tipologia di allegato:
Submitted Version (Pre-print)
Dimensione
371.05 kB
Formato
Adobe PDF
|
371.05 kB | Adobe PDF | Visualizza/Apri |
|
LieGrFP.pdf
Solo gestori archivio
Tipologia di allegato:
Publisher’s Version (Version of Record, VoR)
Dimensione
313.01 kB
Formato
Adobe PDF
|
313.01 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
