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The Quarterly Journal of Mathematics Advance Access originally published online on May 15, 2006
The Quarterly Journal of Mathematics 2006 57(4):425-448; doi:10.1093/qmath/hal007
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© 2006. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

LIE G-TORI OF SYMPLECTIC TYPE

Georgia Benkart1,{dagger} and Yoji Yoshii2 {ddagger}

1 Department of Mathematics, University of Wisconsin, Madison, WI 53706-1388, USA
2 Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075, USA

{dagger} Corresponding author. E-mail: benkart{at}math.wisc.edu


  Abstract

We classify centreless Lie G-tori of type Cr including the most difficult case r = 2 by applying techniques due to Seligman. In particular, we show that the coordinate algebra of a Lie G-torus of type C2 is either an associative G-torus with involution or a Clifford G-torus. Our results generalize the classification of the core of the extended affine Lie algebras of type Cr by Allison and Gao.


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