Lie-algebras of Polynomial-growth

Félix, Yves;Halperin, S.;Thomas, JC.
(1991) Journal of the London mathematical society — Vol. 43, p. 556-566 (1991)

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  • Félix, YvesUCLouvain
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  • Halperin, S.
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  • Thomas, JC.
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Abstract
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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Félix, Y., Halperin, S., & Thomas, JC. (1991). Lie-algebras of Polynomial-growth. Journal of the London mathematical society, 43, 556-566. https://hdl.handle.net/2078.5/45473 (Original work published 1991)