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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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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.
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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