Geodesic
Quaternion Normed Space with Isometry Group $\mathbb{Z}_2$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 90-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a finite-dimensional linear space over the quaternion field, we construct a norm with the following property. Any linear isometry is one of the two transformations $x\mapsto x$ and $x\mapsto-x$.
Keywords: quaternion normed space, isometry. 
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     author = {R. S. Ismagilov and Yu. I. Lyubich},
     title = {Quaternion {Normed} {Space} with {Isometry} {Group~}$\mathbb{Z}_2$},
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R. S. Ismagilov; Yu. I. Lyubich. Quaternion Normed Space with Isometry Group $\mathbb{Z}_2$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 42 (2008) no. 3, pp. 90-92. http://geodesic.mathdoc.fr/item/FAA_2008_42_3_a11/

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