Improved stability for odd-dimensional orthogonal group

preprint2013arXivOpen access

We compute the kernel of the stabilization map for $K_1$ -functors modeled on split Chevalley groups of types $B_l, C_l, E_l$ one step below the stable range. For the groups of type $B_l$ this implies early injective stability for $K_1(B_l, R)$ over a certain class of rings.

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Improved stability for odd-dimensional orthogonal group

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