Contact nilpotent Lie algebras
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- by M. A. Alvarez, M. C. Rodríguez-Vallarte and G. Salgado PDF
- Proc. Amer. Math. Soc. 145 (2017), 1467-1474 Request permission
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
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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
- MR Author ID: 928680
- 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
- MR Author ID: 723863
- ORCID: 0000-0002-8031-8881
- Email: gsalgado@fciencias.uaslp.mx, gil.salgado@gmail.com
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1467-1474
- MSC (2010): Primary 17B5x, 17B30, 53D10
- DOI: https://doi.org/10.1090/proc/13341
- MathSciNet review: 3601539