The cohomology of semisimple Lie algebras with coefficients in a Verma module
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 Trans. Amer. Math. Soc. 240 (1978), 115127 Request permission
Abstract:
The structure of the cohomology of a complex semisimple Lie algebra with coefficients in an arbitrary Verma module is completely determined. Because the Verma modules are infinitedimensional, the cohomology need not vanish (as it does for nontrivial finitedimensional modules). The methods presented exploit the homological machinery of CartanEilenberg [3]. The results of [3], when applied to the universal enveloping algebra of a semisimple Lie algebra and when coupled with key results of Kostant [12], HochschildSerre [9], yield the basic structure theoremTheorem 4.19. Our results show, incidently, that an assertion of H. Kimura, Theorem 2 of [13] is false. A counterexample is presented in §6.References

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Additional Information
 © Copyright 1978 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 240 (1978), 115127
 MSC: Primary 17B10
 DOI: https://doi.org/10.1090/S00029947197804860123
 MathSciNet review: 0486012