Domiaty, Rudolf Z. The group of continuous autotopisms of the loop \(S^ 7\). (Die Gruppe der stetigen Autotopismen des Loops \(S^ 7\).) (German) Zbl 0798.20060 J. Geom. 45, No. 1-2, 51-62 (1992). The unit sphere \(S^ 7\) is a subloop of the multiplicative Moufang loop of the eight-dimensional Cayley algebra \(A\). The author considers continuous pseudoautomorphisms and continuous autotopisms of \(S^ 7\). They are shown to be restrictions of corresponding transformations of \(A\). This yields a description of the related groups. Reviewer: T.Kepka (Praha) MSC: 20N05 Loops, quasigroups 22A30 Other topological algebraic systems and their representations 20E36 Automorphisms of infinite groups Keywords:unit sphere \(S^ 7\); Moufang loop; Cayley algebra; continuous pseudoautomorphisms; continuous autotopisms PDFBibTeX XMLCite \textit{R. Z. Domiaty}, J. Geom. 45, No. 1--2, 51--62 (1992; Zbl 0798.20060) Full Text: DOI References: [1] R.H. BRUCK, A Survey on Binary Systems. Ergebnisse Math., Band 20, Springer-Verlag, Berlin 1966 · Zbl 0141.01401 [2] H.-D.EBBINGHAUS et.al., Zahlen. Grundwissen Math., Band 1, Springer-Verlag, Berlin 1988 [3] E. HEWITT-K.A. ROSS, Abstract Harmonic Analysis I. Grundlehren Math. Wissensch., Band 115, Springer-Verlag, Berlin 1963 · Zbl 0115.10603 [4] G. PICKERT, Projektive Ebenen. Grundlehren Math. Wissensch., Band 80, Springer-Verlag, Berlin 1955 [5] T.A. SPRINGER, Oktaven, Jordan-Algebren und Ausnahmegruppen. (Vorlesung i. SS. 1963, ausgearbeitet von P.Eysenbach.) Mathematisches Institut Göttingen, 1963 [6] G.W. WHITEHEAD, Elements of Homotopy Theory, Graduate Texts Maths., 61, Springer-Verlag, New York 1978 [7] K.A. ZHEVLAKOV et.al., Rings that are Nearly Associative. Academic Press, New York 1982. · Zbl 0487.17001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.