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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on symplectic injective stability


Authors: Rabeya Basu, Pratyusha Chattopadhyay and Ravi A. Rao
Journal: Proc. Amer. Math. Soc. 139 (2011), 2317-2325
MSC (2000): Primary 13C10, 13H05, 19B14, 19B99, 55R50
Published electronically: December 16, 2010
MathSciNet review: 2784796
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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\vert(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\vert 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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Additional Information

Rabeya Basu
Affiliation: Indian Institute of Science Education and Research, Kolkata 741 252, India
Email: rbasu@iiserkol.ac.in

Pratyusha Chattopadhyay
Affiliation: Institute of Mathematical Sciences, Chennai 600 113, India
Email: pratyusha@imsc.res.in

Ravi A. Rao
Affiliation: Tata Institute of Fundamental Research, Mumbai 400 005, India
Email: ravi@math.tifr.res.in

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10654-8
PII: S 0002-9939(2010)10654-8
Keywords: Unimodular rows, elementary symplectic group
Received by editor(s): January 9, 2010
Received by editor(s) in revised form: January 12, 2010, June 9, 2010, and June 18, 2010
Published electronically: December 16, 2010
Communicated by: Martin Lorenz
Article copyright: © Copyright 2010 American Mathematical Society