Classification of minimal algebras over any field up to dimension 6 6

We give a classification of minimal algebras generated in degree 11, defined over any field k\mathbf {k} of characteristic different from 22, up to dimension 66. This recovers the classification of nilpotent Lie algebras over k\mathbf {k} up to dimension 66. In the case of a field k\mathbf {k} of ch...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2011-09, Vol.364 (2), p.1007-1028
Main Authors: Bazzoni, Giovanni, Muñoz, Vicente
Format: Article
Language:English
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Research article
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Summary:We give a classification of minimal algebras generated in degree 11, defined over any field k\mathbf {k} of characteristic different from 22, up to dimension 66. This recovers the classification of nilpotent Lie algebras over k\mathbf {k} up to dimension 66. In the case of a field k\mathbf {k} of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to 66, up to k\mathbf {k}-homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-2011-05471-1