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Transactions of the American Mathematical Society

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

 
 

 

The ascending central series of nilpotent Lie algebras with complex structure


Authors: Adela Latorre, Luis Ugarte and Raquel Villacampa
Journal: Trans. Amer. Math. Soc. 372 (2019), 3867-3903
MSC (2010): Primary 17B30; Secondary 53C30, 53C15
DOI: https://doi.org/10.1090/tran/7512
Published electronically: May 30, 2019
MathSciNet review: 4009385
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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 $(\mathfrak {g}, J)$.


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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.
Article copyright: © Copyright 2019 American Mathematical Society