Nice group structure on the elementary orbit space of unimodular rows

Abstract

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

10 pages

Cited by in corpus (1)

• Zero cycles, Mennicke symbols and ${\mathrm{K}}_1$-stability of certain real affine algebras