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

 

Small infinite dimensional modules
for algebraic groups


Author: Andy R. Magid
Journal: Proc. Amer. Math. Soc. 125 (1997), 75-81
MSC (1991): Primary 20G99
MathSciNet review: 1389530
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Abstract: A infinite dimensional module for an algebraic group is called small provided every proper submodule is finite dimensional. Small infinite dimensional modules exist provided that the characteristic is zero and the group has a non-trivial unipotent radical. The unipotent radical is shown to act through an abelian quotient, which allows a description, up to finite dimensional quotients, of the SID modules with trivial module socle via equivariant commutative algebra. In the case that the group is in fact unipotent, this description is used to calculate the Hilbert function of the ascending socle series of the module.


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Additional Information

Andy R. Magid
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
Email: amagid@uoknor.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03859-8
PII: S 0002-9939(97)03859-8
Received by editor(s): July 31, 1995
Additional Notes: Partially supported by NSA grant MDA904–95–H–1038.
Communicated by: Eric M. Friedlander
Article copyright: © Copyright 1997 American Mathematical Society