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arXiv · 2104.09784

Nice group structure on the elementary orbit space of unimodular rows

Manoj K. Keshari·Sampat Sharma
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Abstract

(1) If $R$ is an affine algebra of dimension $d\geq 4$ over $\overline{\mathbb{F}}_{p}$ with $p>3$, then the group structure on ${\rm Um}_d(R)/{\rm E}_d(R)$ is nice. (2) If $R$ is a commutative noetherian ring of dimension $d\geq 2$ such that ${\rm E}_{d+1}(R)$ acts transitively on ${\rm Um}_{d+1}(R),$ then the group structure on ${\rm Um}_{d+1}(R[X])/{\rm E}_{d+1}(R[X])$ is nice.

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Manoj K. Keshari, Sampat Sharma. 2021-04-20. Nice group structure on the elementary orbit space of unimodular rows. https://doi.org/10.1016/j.jpaa.2021.106889

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