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Classification of Pairs of Rotations in Finite-Dimensional Euclidean Space

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Abstract

A rotation in a Euclidean space V is an orthogonal map δ ∈ O(V) which acts locally as a plane rotation with some fixed angle a(δ) ∈ [0,π]. We give a classification of all finite-dimensional representations of the real algebra \(\mathbb{R}\left\langle X,Y\right\rangle\) that are given by rotations, up to orthogonal isomorphism.

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Authors and Affiliations

  1. Matematiska Institutionen, Uppsala Universitet, Box 480, 75106, Uppsala, Sweden

    Erik Darpö

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  1. Erik Darpö
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Correspondence to Erik Darpö.

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Dedicated to Fred Van Oystaeyen, on the occasion of his sixtieth birthday.

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Darpö, E. Classification of Pairs of Rotations in Finite-Dimensional Euclidean Space. Algebr Represent Theor 12, 333–342 (2009). https://doi.org/10.1007/s10468-009-9156-3

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  • DOI: https://doi.org/10.1007/s10468-009-9156-3

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