Engel conditions and symmetric tensors

Mattarei, Sandro (2011) Engel conditions and symmetric tensors. Linear and Multilinear Algebra, 59 (4). pp. 441-449. ISSN 0308-1087

Full content URL: http://dx.doi.org/10.1080/03081081003621295

Engel conditions and symmetric tensors

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In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Our main result generalizes this in the language of tensor algebra, and describes a relatively small generating set for the module generated by all n-th tensor powers of elements of a finitely generated ℤ-module M, in terms of a generating set for M.

Keywords:Engel condition, Lie ring, symmetrization, tensor
Subjects:G Mathematical and Computer Sciences > G110 Pure Mathematics
Divisions:College of Science > School of Mathematics and Physics
ID Code:18502
Deposited On:11 Dec 2015 09:26

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