| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Cadiz, Dept Matemat, Cadiz - Spain
[2] Univ Fed ABC, CMCC, Santo Andre - Brazil
[3] Univ Coimbra, CeBER Ctr Business & Econ Res, Coimbra - Portugal
[4] Univ Coimbra, CMUC Ctr Math, Coimbra - Portugal
[5] Univ Coimbra, FEUC, Coimbra - Portugal
Total Affiliations: 5
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| Document type: | Journal article |
| Source: | LINEAR & MULTILINEAR ALGEBRA; v. 67, n. 6, p. 1250-1268, JUN 3 2019. |
| Web of Science Citations: | 2 |
| Abstract | |
Let be an arbitrary linear space and an n-linear map. It is proved that, for each choice of a basis of , the n-linear map f induces a (nontrivial) decomposition as a direct sum of linear subspaces of , with respect to . It is shown that this decomposition is f-orthogonal in the sense that when , and in such a way that any is strongly f-invariant, meaning that A sufficient condition for two different decompositions of induced by an n-linear map f, with respect to two different bases of , being isomorphic is deduced. The f-simplicity - an analog of the usual simplicity in the framework of n-linear maps - of any linear subspace of a certain decomposition induced by f is characterized. Finally, an application to the structure theory of arbitrary n-ary algebras is provided. This work is a close generalization the results obtained by Calderon. (AU) | |
| FAPESP's process: | 17/15437-6 - N-ary split strutures |
| Grantee: | Ivan Kaygorodov |
| Support Opportunities: | Scholarships abroad - Research |