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Structurable algebras of skew-dimension one and hermitian cubic norm structures

Tom De Medts (UGent)
(2019) COMMUNICATIONS IN ALGEBRA. 47(1). p.154-172
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Abstract
We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of nonlinear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures. After this work was essentially finished, we became aware of the fact that both descriptions already occur in (somewhat hidden places in) the literature. Nevertheless, we prove some facts that had not been noticed before: We show that every form of a matrix structurable algebra can be described by our constructions; We give explicit formulas for the norm nu; We make a precise connection with the Cayley-Dickson process for structurable algebras.
Keywords
Cayley-Dickson process, cubic norm structures, isotopies, structurable algebras

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MLA
De Medts, Tom. “Structurable Algebras of Skew-dimension One and Hermitian Cubic Norm Structures.” COMMUNICATIONS IN ALGEBRA 47.1 (2019): 154–172. Print.
APA
De Medts, T. (2019). Structurable algebras of skew-dimension one and hermitian cubic norm structures. COMMUNICATIONS IN ALGEBRA, 47(1), 154–172.
Chicago author-date
De Medts, Tom. 2019. “Structurable Algebras of Skew-dimension One and Hermitian Cubic Norm Structures.” Communications in Algebra 47 (1): 154–172.
Chicago author-date (all authors)
De Medts, Tom. 2019. “Structurable Algebras of Skew-dimension One and Hermitian Cubic Norm Structures.” Communications in Algebra 47 (1): 154–172.
Vancouver
1.
De Medts T. Structurable algebras of skew-dimension one and hermitian cubic norm structures. COMMUNICATIONS IN ALGEBRA. 2019;47(1):154–72.
IEEE
[1]
T. De Medts, “Structurable algebras of skew-dimension one and hermitian cubic norm structures,” COMMUNICATIONS IN ALGEBRA, vol. 47, no. 1, pp. 154–172, 2019.
@article{8616791,
  abstract     = {We study structurable algebras of skew-dimension one. We present two different equivalent constructions for such algebras: one in terms of nonlinear isotopies of cubic norm structures, and one in terms of hermitian cubic norm structures. After this work was essentially finished, we became aware of the fact that both descriptions already occur in (somewhat hidden places in) the literature. Nevertheless, we prove some facts that had not been noticed before: We show that every form of a matrix structurable algebra can be described by our constructions; We give explicit formulas for the norm nu; We make a precise connection with the Cayley-Dickson process for structurable algebras.},
  author       = {De Medts, Tom},
  issn         = {0092-7872},
  journal      = {COMMUNICATIONS IN ALGEBRA},
  keywords     = {Cayley-Dickson process,cubic norm structures,isotopies,structurable algebras},
  language     = {eng},
  number       = {1},
  pages        = {154--172},
  title        = {Structurable algebras of skew-dimension one and hermitian cubic norm structures},
  url          = {http://dx.doi.org/10.1080/00927872.2018.1468905},
  volume       = {47},
  year         = {2019},
}

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