A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process

  • R. Boboescu Ovid-universitetet i Constanta, Romania
  • C. Flaut Ovid-universitetet i Constanta, Romania
Keywords: Cayley-Dickson algebras; twisted group algebras; nonassociative quaternion algebras;


UDC 512.55

Starting from some ideas given in [J. W. Bales, A tree for computing the Cayley–Dickson twist, Missouri J. Math. Sci., 21, No. 2, 83–93 (2009)], in this paper we present an algorithm for computing the elements of the basis in an algebra obtained by the Cayley–Dickson process.  As a consequence of this result, we prove that an algebra obtained by the Cayley–Dickson process is a twisted group algebra for the group $G=\mathbb{Z}_{2}^{n},n=2^{t}$, $t\in \mathbb{N}$, over a field $K$ with ${\rm char} K\neq 2$.  We give some properties and applications of the quaternion nonassociative algebras. 

Author Biography

R. Boboescu, Ovid-universitetet i Constanta, Romania




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How to Cite
Boboescu, R., and C. Flaut. “A Twisted Group Algebra Structure for an Algebra Obtained by the Cayley – Dickson Process”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 6, July 2022, pp. 752 -60, doi:10.37863/umzh.v74i6.6949.
Research articles