Structure of a twisted group algebra for an algebra obtained by the Cayley-Dickson process. (English. Ukrainian original) Zbl 1523.16030

Ukr. Math. J. 74, No. 6, 859-870 (2022); translation from Ukr. Mat. Zh. 74, No. 6, 761-771 (2022).
Summary: Following some ideas proposed in [J. W. Bales, Missouri J. Math. Sci. 21, No. 2, 83–93 (2009; Zbl 1187.17002)], we present an algorithm for computing basis elements in an algebra obtained by the Cayley-Dickson process. As a consequence of this result, we prove that an algebra obtained with the help of 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 \(\operatorname{char}(K \neq 2)\). We also present some properties and applications of the quaternion nonassociative algebras.


16S35 Twisted and skew group rings, crossed products
16S34 Group rings


Zbl 1187.17002
Full Text: DOI


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