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

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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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
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Deposited On:31 Oct 2012 09:40
Last Modified:07 Feb 2014 09:38

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