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Journal of the London Mathematical Society 1991 s2-43(3):556-566; doi:10.1112/jlms/s2-43.3.556
© 1991 by London Mathematical Society
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© Oxford University Press

Lie Algebras of Polynomial Growth

Yves Félix, Stephen Halperin and Jean-Claude Thomas

Institute de Mathématiques, Université Catholique de Louvain B1348 Louvain-la-Neuve, Belgium
Physical Sciences Division, Scarborough College, University of Toronto Scarborough, Canada M1C 1A4
U.F.R. de Mathématiques, Université de Lille, Flandres, Artois 59655 Villeneuve d'Ascq, France

Kac has introduced the notion of (polynomial) growth for a graded Lie algebra. Here we consider Lie algebras L that occur as ideals either in the rational homotopy Lie algebra of a simply connected CW complex of finite type and finite category or as ideals in the homotopy Lie algebra of a local noetherian ring. Theorem. If these ideals have (finite) polynomial growth, then they are finite dimensional.


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