SOME REMARKS ON SYMPLECTIC INJECTIVE STABILITY

作者：Basu Rabeya^*; Chattopadhyay Pratyusha; Rao Ravi A

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 139(7): 2317-2325.

DOI：10.1090/S0002-9939-2010-10654-8

• Unimodular rows
• elementary symplectic group

It is shown that if A is an affine algebra of odd dimension d over an infinite field of cohomological dimension at most one, with (d +1)!A = A, and with 4 vertical bar(d - 1), then Um(d+1)(A) = e(1)Sp(d+1)(A). As a consequence it is shown that if A is a non-singular affine algebra of dimension d over an infinite field of cohomological dimension at most one, and d!A = A, and 4 vertical bar d, then Sp(d)(A) boolean AND ESp(d+2)(A) = ESp(d)(A). This result is a partial analogue for even-dimensional algebras of the one obtained by Basu and Rao for odd-dimensional algebras earlier.

• 出版日期2011-7