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A refinement of the toral rank conjecture for 2-step nilpotent Lie algebras

Author: Paulo Tirao
Journal: Proc. Amer. Math. Soc. 128 (2000), 2875-2878
MSC (2000): Primary 17B56, 17B30
Published electronically: April 28, 2000
MathSciNet review: 1664387
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It is known that the total (co)-homoloy of a 2-step nilpotent Lie algebra $\mathfrak{g}$ is at least $2^{\vert\mathfrak{z}\vert}$, where $\mathfrak{z}$is the center of $\mathfrak{g}$. We improve this result by showing that a better lower bound is $2^t$, where $t={\vert\mathfrak{z}\vert+\left[\frac{\vert v\vert+1}2\right]}$ and $v$ is a complement of $\mathfrak{z}$ in $\mathfrak{g}$. Furthermore, we provide evidence that this is the best possible bound of the form $2^t$.

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Additional Information

Paulo Tirao
Affiliation: International Centre for Theoretical Physics (ICTP), Trieste, Italy; Facultad de Matemática, Astronomía y Física, Córdoba, Argentina
Address at time of publication: Heinrich-Heine-Universität, Mathematisches Institut, 40225 Düsseldorf, Germany

Keywords: Homology of Lie algebras, 2-step nilpotent Lie algebras, toral rank conjecture
Received by editor(s): August 24, 1998
Received by editor(s) in revised form: November 22, 1998
Published electronically: April 28, 2000
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society

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