Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/89499
DC Field | Value | Language |
---|---|---|
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.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
item.openairetype | article | - |
item.cerifentitytype | Publications | - |
item.grantfulltext | open | - |
item.fulltext | Com Texto completo | - |
item.languageiso639-1 | en | - |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
Decompositions of linear spaces induced by n_linear maps_AC_IK_PS_repositorio_UC.pdf | 342.43 kB | Adobe PDF | View/Open |
SCOPUSTM
Citations
4
checked on Apr 15, 2024
WEB OF SCIENCETM
Citations
10
3
checked on Apr 2, 2024
Page view(s)
167
checked on Apr 16, 2024
Download(s)
88
checked on Apr 16, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.