A nice group structure on the orbit space of unimodular rows |
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| Authors: | Anuradha S Garge and Ravi A Rao |
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| Institution: | (1) Department of Mathematics, University of Pune, Aniket Soc. No. 2, House Number 16, Bibawewadi Road, Ganeshkhind, Pune, 411 037, India;(2) School of Mathematics, Tata Institute of Fundamental Research, Dr. Homi Bhabha Road, Mumbai, 400 005, India |
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| Abstract: | If A is an affine algebra of dimension d ≥ 2, over a perfect field k, where char k ≠ 2 and c.d.2
k ≤ 1, or if A = RX], where R is a local, noetherian ring of dimension d ≥ 2, in which 2R = R, then the group structure of W. van der Kallen on the orbit space Um
d+1(A)/E
d+1(A) is given by coordinatewise multiplication via the product formula
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| Keywords: | Unimodular row Stable dimension Vaserstein symbol Mennicke symbol Elementary symplectic Witt group |
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![$$(a, a_1, \ldots, a_d)] * (b, a_1, \ldots, a_d)]=(ab, a_1, \ldots, a_d)].$$](/content/w3307571g441l362/10977_2007_9011_Article_Equa.gif)