Exponential growth of lie algebras of finite global dimension

Félix, Yves;Halperin, Steve;Thomas, Jean-Claude
(2007) Proceedings of the American Mathematical Society — Vol. 135, n° 5, p. 1575-1578 (2007)

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Authors
  • Félix, YvesUCLouvain
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  • Halperin, Steve
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  • Thomas, Jean-Claude
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Abstract
Let L be a connected finite type graded Lie algebra. If dim L = infinity and gldimL < infinity, then log index L = alpha > 0. If, moreover, alpha < infinity, then for some Sigma(d-1)(i=1) dim Lk+i = e(k alpha k), where alpha(k) -> log index L as k -> infinity.
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Félix, Y., Halperin, S., & Thomas, J.-C. (2007). Exponential growth of lie algebras of finite global dimension. Proceedings of the American Mathematical Society, 135(5), 1575-1578. https://doi.org/10.1090/S0002-9939-07-08721-7 (Original work published 2007)