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Exponential growth of Lie algebras of finite global dimension

Authors:	Yves Felix Steve Halperin Jean-Claude Thomas

Institution:	Institut Mathematique, Université Catholique de Louvain, 2, Chemin du Cyclotron, 1348, Louvain-La-Neuve, Belgium Steve Halperin ; Department of Mathematics, University of Maryland, College Park, Maryland 20742-3281 Jean-Claude Thomas ; Faculté des Sciences, Université d'Angers, 49045 Bd Lavoisier, Angers, France

Abstract:	Let 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 , $\sum_{i=1}^{d-1}$ dim $\, L_{k+i} = e^{k\alpha_k}\,,\,\,$ where $\alpha_k \to$ log index as $k\to \infty\,.$

Keywords:	Homotopy Lie algebra graded Lie algebra global dimension exponential growth

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