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Linear and Multilinear Algebra Volume 67, 2019 - Issue 6
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Original Articles

Decompositions of linear spaces induced by n-linear maps

Antonio Jesús CalderónDepartamento de Matemáticas, Universidad de Cádiz, Cádiz, España.View further author information
,
Ivan KaygorodovCMCC, Universidade Federal do ABC, Santo André, Brasil.Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0003-2084-9215View further author information
ORCID Icon &
Paulo SaraivaCeBER-Centre for Business and Economics Research, University of Coimbra, Coimbra, Portugal.;CMUC-Centre for Mathematics, University of Coimbra, Coimbra, Portugal.;FEUC, Universidade de Coimbra, Coimbra, Portugal.ORCID Iconhttp://orcid.org/0000-0002-2856-5033View further author information
ORCID Icon
Pages 1250-1268 | Received 04 Feb 2018, Accepted 07 Mar 2018, Published online: 20 Mar 2018

References

  • Calderón AJ . Decompositions of linear spaces induced by bilinear maps. Linear Algebra Appl. 2018;542:209–224.
  • Calderón A , Navarro FJ . Arbitrary algebras with a multiplicative basis. Linear Algebra Appl. 2016;498:106–116.
  • Calderón AJ . Associative algebras admitting a quasi-multiplicative basis. Algebr Represent Theory. 2014;17(6):1889–1900.
  • Barreiro E , Calderón A , Kaygorodov I , et al. n-Ary generalized Lie-type color algebras admitting a quasi-multiplicative basis, arXiv:1801.02071.
  • Barreiro E , Kaygorodov I , Sánchez JM . k-Modules over linear spaces by n-linear maps admitting a multiplicative basis, arXiv:1707.07483.
  • Calderón AJ , Navarro, FJ , Sánchez JM . n-Algebras admitting a multiplicative basis. J Algebra Appl. 2018;16:11, 1850025. 11 p.
  • Calderón AJ . Lie algebras with a set grading. Linear Algebra Appl. 2014;452:7–20.
  • Cao Y , Chen LY . On the structure of graded Leibniz triple systems. Linear Algebra Appl. 2016;496:496–509.
  • Filippov V . n-Lie algebras. Sib Math J. 1985;26(6):126–140.
  • Kaygorodov I , Pozhidaev A , Saraiva P . On a ternary generalization of Jordan algebras. Linear Multilinear algebra. DOI:10.1080/03081087.2018.1443426
  • Pozhidaev A . n-ary Mal’tsev algebras. Algebra Logic. 2001;40(3):309–329.

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