Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/89499
DC Field | Value | Language |
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dc.contributor.author | Calderón, Antonio Jesús | - |
dc.contributor.author | Kaygorodov, Ivan | - |
dc.contributor.author | Saraiva, Paulo | - |
dc.date.accessioned | 2020-06-12T14:27:17Z | - |
dc.date.available | 2020-06-12T14:27:17Z | - |
dc.date.issued | 2019 | - |
dc.identifier.uri | https://hdl.handle.net/10316/89499 | - |
dc.description.abstract | Let V be an arbitrary linear space and f : V x ... x V \rightarrow V an n-linear map. It is proved that, for each choice of a basis B of V, the n-linear map f induces a (nontrivial) decomposition V = \oplus V_j as a direct sum of linear subspaces of V, with respect to B. It is shown that this decomposition is f-orthogonal in the sense that 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, meaning that f(V, ..., V_j, ..., V) \subset V_j. A sufficient condition for two different decompositions of V induced by an n-linear map f, with respect to two different bases of V, being isomorphic is deduced. The f-simplicity - an analogue of the usual simplicity in the framework of n-linear maps - of any linear subspace V_j 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 Calderón (2018). | pt |
dc.language.iso | eng | pt |
dc.publisher | Taylor & Francis | pt |
dc.relation | UID/MAT/00324/2019 | pt |
dc.rights | embargoedAccess | pt |
dc.subject | Linear space, n-linear map, orthogonality, invariant subspace, decomposition theorem. | pt |
dc.title | Decompositions of linear spaces induced by n-linear maps | pt |
dc.type | article | - |
degois.publication.firstPage | 1250 | pt |
degois.publication.lastPage | 1268 | pt |
degois.publication.issue | 6 | pt |
degois.publication.title | Linear and Multilinear Algebra | pt |
dc.relation.publisherversion | https://www.tandfonline.com/doi/abs/10.1080/03081087.2018.1450829?journalCode=glma20 | pt |
dc.peerreviewed | yes | pt |
dc.identifier.doi | 10.1080/03081087.2018.1450829 | pt |
degois.publication.volume | 67 | pt |
dc.date.embargo | 2020-01-01 | * |
uc.date.periodoEmbargo | 365 | pt |
item.openairetype | article | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
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Decompositions of linear spaces induced by n_linear maps_AC_IK_PS_repositorio_UC.pdf | 342.43 kB | Adobe PDF | View/Open |
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