Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

Contact nilpotent Lie algebras


Authors: M. A. Alvarez, M. C. Rodríguez-Vallarte and G. Salgado
Journal: Proc. Amer. Math. Soc. 145 (2017), 1467-1474
MSC (2010): Primary 17B5x, 17B30, 53D10
DOI: https://doi.org/10.1090/proc/13341
Published electronically: October 26, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this work we show that for $ n\geq 1$, every finite $ (2n+3)$-dimensional contact nilpotent Lie algebra $ \mathfrak{g}$ can be obtained as a double extension of a contact nilpotent Lie algebra $ \mathfrak{h}$ of codimension 2. As a consequence, for $ n\geq 1$, every $ (2n+3)$-dimensional contact nilpotent Lie algebra $ \mathfrak{g}$ can be obtained from the 3-dimensional Heisenberg Lie algebra $ \mathfrak{h}_3$, by applying a finite number of successive series of double extensions. As a byproduct, we obtain an alternative proof of the fact that a $ (2n+1)$-nilpotent Lie algebra $ \mathfrak{g}$ is a contact Lie algebra if and only if it is a central extension of a nilpotent symplectic Lie algebra.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 17B5x, 17B30, 53D10

Retrieve articles in all journals with MSC (2010): 17B5x, 17B30, 53D10


Additional Information

M. A. Alvarez
Affiliation: Departamento de Matemáticas, Universidad de Antofagasta, Antofagasta, Chile
Email: maria.alvarez@uantof.cl

M. C. Rodríguez-Vallarte
Affiliation: Facultad de Ciencias, UASLP, Av. Salvador Nava s/n, Zona Universitaria, CP 78290, San Luis Potosí, S.L.P., México
Email: mcvallarte@fc.uaslp.mx

G. Salgado
Affiliation: Facultad de Ciencias, UASLP, Av. Salvador Nava s/n, Zona Universitaria, CP 78290, San Luis Potosí, S.L.P., México
Email: gsalgado@fciencias.uaslp.mx, gil.salgado@gmail.com

DOI: https://doi.org/10.1090/proc/13341
Received by editor(s): May 6, 2016
Received by editor(s) in revised form: June 15, 2016
Published electronically: October 26, 2016
Additional Notes: The first author was supported in part by Becas Iberoamérica de Jóvenes Profesores e Investigadores, Santander Universidades, and Postdoctoral Fellowship from Centro de Investigación en Matemáticas.
The second author was supported by CONACyT Grants 154340, 222870 and PROMEP Grant UASLP-CA-228.
The third author was supported by CONACyT Grant 222870 and PROMEP Grant UASLP-CA-228.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2016 American Mathematical Society