Some remarks on spin-orbits of unit vectors
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For n ∈ N and a commutative ring R with 2 ∈ R×, the group SLn(R) acts on the set U mn(R) of unimodular vectors of length n and Spin2n(R) acts on the set of unit vectors U2n−1(R). We give an example of a ring for which the comparison map U mn(R)/SLn(R) → U2n−1(R)/Spin2n(R) fails to be bijective.
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Journal of pure and applied algebra, 229, 1, Elsevier, Amsterdam, 2024, https://doi.org/10.1016/j.jpaa.2024.107802