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.
Articolo in rivista - Articolo scientifico
Mathematics (all)
English
2015
205
1
185
209
partially_open
Weigel, T. (2015). Graded Lie algebras of type FP. ISRAEL JOURNAL OF MATHEMATICS, 205(1), 185-209 [10.1007/s11856-014-1131-y].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/83693
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