Recent zbMATH articles in MSC 17Chttps://www.zbmath.org/atom/cc/17C2021-02-27T13:50:00+00:00Unknown authorWerkzeugStatement of retraction: Eight-dimensional octonion-like but associative normed division algebra.https://www.zbmath.org/1453.160162021-02-27T13:50:00+00:00The editors and publisher have retracted the article [\textit{J. Christian}, Commun. Algebra 49, No. 2, 905--914 (2021; Zbl 1453.16017)]. The error is obvious both from the title and abstract, which claims to construct an 8-dimensional normed division algebra over \(\mathbb R\), which doesn't exist due to Hurwitz's theorem [\textit{A. Hurwitz}, Math. Ann. 88, 1--25 (1922; JFM 48.1164.03)].Deducing the symmetry of the standard model from the automorphism and structure groups of the exceptional Jordan algebra.https://www.zbmath.org/1453.810362021-02-27T13:50:00+00:00"Todorov, Ivan"https://www.zbmath.org/authors/?q=ai:todorov.ivan-t"Dubois-Violette, Michel"https://www.zbmath.org/authors/?q=ai:dubois-violette.michelRetracted: Eight-dimensional octonion-like but associative normed division algebra.https://www.zbmath.org/1453.160172021-02-27T13:50:00+00:00"Christian, Joy"https://www.zbmath.org/authors/?q=ai:christian.joySummary: We present an eight-dimensional even sub-algebra of the \(2^4=16\)-dimensional associative Clifford algebra \(Cl_{4,0}\) and show that its eight-dimensional elements denoted as \(\mathbf X\) and \(\mathbf Y\) respect the norm relation \(\|\mathbf X \mathbf Y\| = \|\mathbf X\| \|\mathbf Y\|\) thus forming an octonion-like but associative normed division algebra, where the norms are calculated using the fundamental geometric product instead of the usual scalar product. The corresponding 7-sphere has a topology that differs from that of octonionic 7-sphere.
Editorial remark. This article has been retracted by the Editors and Publisher. The error is obvious both from the title and abstract, which claims to construct an 8-dimensional normed division algebra over \(\mathbb R\), which doesn't exist due to Hurwitz's theorem [\textit{A. Hurwitz}, Math. Ann. 88, 1--25 (1922; JFM 48.1164.03)].