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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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

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