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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Exponential growth of Lie algebras of finite global dimension


Authors: Yves Felix, Steve Halperin and Jean-Claude Thomas
Journal: Proc. Amer. Math. Soc. 135 (2007), 1575-1578
MSC (2000): Primary 55P35, 55P62, 17B70
Published electronically: January 8, 2007
MathSciNet review: 2276669
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Abstract: Let $ L$ be a connected finite type graded Lie algebra. If dim $ L = \infty$ and gldim $ \, L<\infty$, then log index $ \, L=\alpha >0$. If, moreover, $ \alpha<\infty$, then for some $ d$, $ \sum_{i=1}^{d-1}$   dim$ \, L_{k+i} = e^{k\alpha_k}\,,\,\, $ where $ \alpha_k \to $ log index $ L$ as $ k\to \infty\,.$


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Additional Information

Yves Felix
Affiliation: Institut Mathematique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348, Louvain-La-Neuve, Belgium

Steve Halperin
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742-3281

Jean-Claude Thomas
Affiliation: Faculté des Sciences, Université d’Angers, 49045 Bd Lavoisier, Angers, France

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08721-7
PII: S 0002-9939(07)08721-7
Keywords: Homotopy Lie algebra, graded Lie algebra, global dimension, exponential growth.
Received by editor(s): June 25, 2005
Received by editor(s) in revised form: February 16, 2006
Published electronically: January 8, 2007
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society