Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Decompositions of linear spaces induced by n-linear maps
Publication Date:	2018-01-24
Authors:	- Antonio Jesus Calderón - Ivan Kaygorodov - Paulo Saraiva
Abstract:	Let V be an arbitrary linear space and f : V × ... × V → V an n-linear map. We show that, for any choice of basis B of V, the n-linear map f induces on V a decomposition (depending on B) V = ⊕V_j as a direct sum of linear subspaces, which is f-orthogonal in the sense f(V,...,V_j,...,V_k,...,V) = 0 when j \neq k, and in such a way that any V_j is strongly f-invariant in the sense f(V,...,V_j,...,V) ⊂ V_j. We also characterize the f-simplicity of any V_j. Finally, an application to the structure theory of arbitrary n-ary algebras is also provided. It is the full generalization of some early result [6].
Institution:	DMUC 18-04
Online version:	http://www.mat.uc.pt...prints/eng_2018.html
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