Classification of minimal algebras over any field up to dimension $6$
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- by Giovanni Bazzoni and Vicente Muñoz PDF
- Trans. Amer. Math. Soc. 364 (2012), 1007-1028 Request permission
Abstract:
We give a classification of minimal algebras generated in degree $1$, defined over any field $\mathbf {k}$ of characteristic different from $2$, up to dimension $6$. This recovers the classification of nilpotent Lie algebras over $\mathbf {k}$ up to dimension $6$. In the case of a field $\mathbf {k}$ of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to $6$, up to $\mathbf {k}$-homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure.References
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Additional Information
- Giovanni Bazzoni
- Affiliation: Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera 13-15, 28049 Madrid, Spain
- Email: gbazzoni@icmat.es
- Vicente Muñoz
- Affiliation: Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain
- Email: vicente.munoz@mat.ucm.es
- Received by editor(s): May 28, 2010
- Received by editor(s) in revised form: September 16, 2010
- Published electronically: September 15, 2011
- Additional Notes: This research was partially supported by Spanish grant MICINN ref. MTM2007-63582.
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 364 (2012), 1007-1028
- MSC (2010): Primary 55P62, 17B30; Secondary 22E25
- DOI: https://doi.org/10.1090/S0002-9947-2011-05471-1
- MathSciNet review: 2846361