Exponential growth of Lie algebras of finite global dimension
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- by Yves Felix, Steve Halperin and Jean-Claude Thomas PDF
- Proc. Amer. Math. Soc. 135 (2007), 1575-1578 Request permission
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 $d$, $\sum _{i=1}^{d-1} \mbox {\textrm {dim}} L_{k+i} = e^{k\alpha _k} ,$ where $\alpha _k \to$ log index $L$ as $k\to \infty .$References
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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
- 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
- © Copyright 2007 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 135 (2007), 1575-1578
- MSC (2000): Primary 55P35, 55P62, 17B70
- DOI: https://doi.org/10.1090/S0002-9939-07-08721-7
- MathSciNet review: 2276669