Decompositions of linear spaces induced by n-linear maps

Autor(es)

Jesus Calderon, Antonio ^[1] ; Kaygorodov, Ivan ^[2] ; Saraiva, Paulo ^{[3, 4, 5]}

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: LINEAR & MULTILINEAR ALGEBRA; v. 67, n. 6, p. 1250-1268, JUN 3 2019.
• Citações Web of Science: 2

Resumo

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)

• Processo FAPESP: 17/15437-6 - Estruturas n-árias split
• Beneficiário: Ivan Kaygorodov
• Modalidade de apoio: Bolsas no Exterior - Pesquisa