Some remarks on symplectic injective stability

Basu, Rabeya; Chattopadhyay, Pratyusha; Rao, Ravi

doi:10.1090/S0002-9939-2010-10654-8

Some remarks on symplectic injective stability
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by Rabeya Basu, Pratyusha Chattopadhyay and Ravi A. Rao PDF

Proc. Amer. Math. Soc. 139 (2011), 2317-2325 Request permission

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 Um$_{d+1}(A) = e_1\textrm {Sp}_{d+1}(A)$. 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 $4|d$, then $\textrm {Sp}_d(A) \cap \textrm {ESp}_{d+2}(A) = \textrm {ESp}_d(A)$. This result is a partial analogue for even-dimensional algebras of the one obtained by Basu and Rao for odd-dimensional algebras earlier.

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