A homology vanishing theorem for Kac-Moody algebras with coefficients in the category \(\mathcal O\)

DOI10.1016/0021-8693(86)90118-3zbMath0633.17012OpenAlexW2165251985MaRDI QIDQ1096002

Shrawan Kumar

Publication date: 1986

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(86)90118-3

zbMATH Keywords

Verma moduleCasimir operatorcategory Ocomputation of homologysymmetrizable Kac-Moody Lie algebraintegrable highest weight moduleChari-Ilangovan completionhomology vanishing theoremKostant's theorem

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Homological methods in Lie (super)algebras (17B55) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (5)

Cohomology groups of infinite dimensional algebras ⋮ Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras ⋮ Extension of the category \({\mathcal O}^ g\) and a vanishing theorem for the Ext functor for Kac-Moody algebras ⋮ Coproduct for Yangians of affine Kac-Moody algebras ⋮ The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. I: The existence of the resolution

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