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Annihilation Theorem and Separation Theorem for basic classical Lie superalgebras


Author: Maria Gorelik
Journal: J. Amer. Math. Soc. 15 (2002), 113-165
MSC (2000): Primary 17B10, 17B20, 17B35
DOI: https://doi.org/10.1090/S0894-0347-01-00382-4
Published electronically: September 19, 2001
MathSciNet review: 1862799
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Abstract: In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.


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Additional Information

Maria Gorelik
Affiliation: Department of Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Email: gorelik@wisdom.weizmann.ac.il

DOI: https://doi.org/10.1090/S0894-0347-01-00382-4
Keywords: Basic classical Lie superalgebra, adjoint action, Verma module
Received by editor(s): December 6, 2000
Published electronically: September 19, 2001
Additional Notes: The author was partially supported by TMR Grant No. FMRX-CT97-0100. Research at MSRI was supported in part by NSF grant DMS-9701755
Article copyright: © Copyright 2001 American Mathematical Society

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