The cohomology of semisimple Lie algebras with coefficients in a Verma module
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- by Floyd L. Williams PDF
- Trans. Amer. Math. Soc. 240 (1978), 115-127 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 infinite-dimensional, the cohomology need not vanish (as it does for nontrivial finite-dimensional modules). The methods presented exploit the homological machinery of Cartan-Eilenberg [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], Hochschild-Serre [9], yield the basic structure theorem-Theorem 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), 115-127
- MSC: Primary 17B10
- DOI: https://doi.org/10.1090/S0002-9947-1978-0486012-3
- MathSciNet review: 0486012