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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The ascending central series of nilpotent Lie algebras with complex structure
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by Adela Latorre, Luis Ugarte and Raquel Villacampa PDF
Trans. Amer. Math. Soc. 372 (2019), 3867-3903 Request permission

Abstract:

We obtain several restrictions on the terms of the ascending central series of a nilpotent Lie algebra $\mathfrak {g}$ under the presence of a complex structure $J$. In particular, we find a bound for the dimension of the center of $\mathfrak {g}$ when it does not contain any non-trivial $J$-invariant ideal. Thanks to these results, we provide a structural theorem describing the ascending central series of 8-dimensional nilpotent Lie algebras $\mathfrak {g}$ admitting this particular type of complex structure $J$. Since our method is constructive, it allows us to describe the complex structure equations that parametrize all such pairs $(\mathfrak {g}, J)$.
References
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Additional Information
  • Adela Latorre
  • Affiliation: Centro Universitario de la Defensa - I.U.M.A., Academia General Militar, Crta. de Huesca s/n, 50090 Zaragoza, Spain
  • MR Author ID: 1034201
  • Email: adela@unizar.es
  • Luis Ugarte
  • Affiliation: Departamento de Matemáticas - I.U.M.A., Universidad de Zaragoza, Campus Plaza San Francisco, 50009 Zaragoza, Spain
  • MR Author ID: 614982
  • Email: ugarte@unizar.es
  • Raquel Villacampa
  • Affiliation: Centro Universitario de la Defensa - I.U.M.A., Academia General Militar, Crta. de Huesca s/n, 50090 Zaragoza, Spain
  • MR Author ID: 836353
  • Email: raquelvg@unizar.es
  • Received by editor(s): September 21, 2017
  • Published electronically: May 30, 2019
  • Additional Notes: This work was partially supported by the projects MINECO (Spain) MTM2014-58616-P and Gobierno de Aragón/Fondo Social Europeo–Grupo Consolidado E15 Geometría.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 372 (2019), 3867-3903
  • MSC (2010): Primary 17B30; Secondary 53C30, 53C15
  • DOI: https://doi.org/10.1090/tran/7512
  • MathSciNet review: 4009385