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

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Bazzoni, Giovanni and Muñoz, Vicente (2012) Classification of minimal algebras over any field up to dimension 6. Transactions of the American Mathematical Society, 364 (2). pp. 1007-1028. ISSN 0002-9947

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Official URL: http://www.ams.org/journals/tran/2012-364-02/S0002-9947-2011-05471-1/S0002-9947-2011-05471-1.pdf


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Abstract

We give a classification of minimal algebras generated in degree 1, defined over any field k of characteristic different from 2, up to dimension 6. This recovers the classification of nilpotent Lie algebras over k up to dimension 6. In the case of a field k of characteristic zero, we obtain the classification of nilmanifolds of dimension less than or equal to 6, up to k-homotopy type. Finally, we determine which rational homotopy types of such nilmanifolds carry a symplectic structure.


Item Type:Article
Uncontrolled Keywords:Nilmanifolds; rational homotopy; Nilpotent Lie algebras; Minimal model
Subjects:Sciences > Mathematics > Topology
ID Code:16956
Deposited On:31 Oct 2012 09:40
Last Modified:12 Dec 2018 15:12

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