Some remarks on symplectic injective stability

Abstract

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|(d - 1), then Umd+1(A) = e1Spd+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| d, then Spd(A) n ESpd+2(A) = ESpd(A). This result is a partial analogue for evendimensional algebras of the one obtained by Basu and Rao for odd-dimensional algebras earlier. © 2010 American Mathematical Society.