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

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- by Paulo Tirao
- Proc. Amer. Math. Soc.
**128**(2000), 2875-2878 - DOI: https://doi.org/10.1090/S0002-9939-00-05366-1
- Published electronically: April 28, 2000
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## Abstract:

It is known that the total (co)-homoloy of a 2-step nilpotent Lie algebra $\mathfrak {g}$ is at least $2^{|\mathfrak {z}|}$, where $\mathfrak {z}$ is the center of $\mathfrak {g}$. We improve this result by showing that a better lower bound is $2^t$, where $t={|\mathfrak {z}|+\left [\frac {|v|+1}2\right ]}$ 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 $2^t$.## References

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## Bibliographic 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
- Email: ptirao@bart.cs.uni-duesseldorf.de, Paulo.Tirao@FamaF.uncor.edu.ar
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**128**(2000), 2875-2878 - MSC (2000): Primary 17B56, 17B30
- DOI: https://doi.org/10.1090/S0002-9939-00-05366-1
- MathSciNet review: 1664387