A twisted group algebra structure for an algebra obtained by the Cayley – Dickson process
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....
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| Datum: | 2022 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/6949 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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.  |
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| DOI: | 10.37863/umzh.v74i6.6949 |