@UNPUBLISHED{publication1,
title = "Decompositions of linear spaces induced by n-linear maps",
author = "{CALDER{\'{O}}N MART{\'{I}}N, Antonio J.} and {KAYGORODOV, Ivan} and {SARAIVA, Paulo}",
year = "2018-01-24",
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 $\backslash$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]. ",
url = "http://www.mat.uc.pt/preprints/eng\_2018.html",
note = ""
}