


Decompositions of linear spaces induced by nlinear maps
(Preprint)

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Type:

Preprint

National /International:

International

Title: 
Decompositions of linear spaces induced by nlinear maps

Publication Date:

20180124

Authors:

 Antonio J. Calderón Martín
 Ivan Kaygorodov
 Paulo Saraiva

Abstract:

Let V be an arbitrary linear space and f : V × ... × V → V an nlinear map. We show that, for any choice of basis B of V, the nlinear map f induces on V a decomposition (depending on B) V = ⊕V_{j} as a direct sum of linear subspaces, which is forthogonal 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 finvariant in the sense f(V,...,V_{j},...,V) ⊂ V_{j}. We also characterize the fsimplicity of any V_{j}. Finally, an application to the structure theory of arbitrary nary algebras is also provided. It is the full generalization of some early result [6].

Institution:

DMUC 1804

Online version:

http://www.mat.uc.pt...prints/eng_2018.html

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