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On Level 0 Affine Lie Modules

Published online by Cambridge University Press:  20 November 2018

D. J. Britten  and
F. W. Lemire
D. J. Britten
Affiliation:
Department of Mathematics and Statistics, University of Windsor Windsor, Ontario
F. W. Lemire
Affiliation:
Department of Mathematics and Statistics, University of Windsor Windsor, Ontario
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Abstract

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It is proven that the dimensions of the homogeneous summands of a nontrivial Z graded module for an infinité dimensional Heisenberg algebra on which a central element acts as nonzero scalar are unbounded. This result is then applied to show that the central elements of an affine Lie algebra act trivially on any indecomposable diagonalizable module whose weight spaces are of bounded dimension.

Keywords

17B67
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 310 - 314
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Britten, D. J., Lemire, F. W. and Zorzitto, F., Pointed torsion free modules for affine Lie algebras, Comm. Alg. 18(1990), 3307–3321.Google Scholar
2. Chari, Vyjayanthi Integrable representations of affine Lie-algebras, J. Algebra 133(1988), 438–464.Google Scholar
3. Chari, Vyjayanthi and Pressley, Andrew, Integrable representations of twisted affine Lie-algebras, Invent. Math. 85(1986), 317–335.Google Scholar
4. Chari, Vyjayanthi and Pressley, Andrew, Integrable representations of Kac-Moody algebras: Results and open problems, Infinite Dimensional Lie Algebras and Groups, Advanced series in Mathematical Physics, (ed. Victor Kac), World Scientific, 1988.Google Scholar
5. Kac, Victor G., Infinite dimensional Lie algebras, Cambridge Press, 1988.Google Scholar