Cohomology of nilradicals of Borel subalgebras
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- by George F. Leger and Eugene M. Luks
- Trans. Amer. Math. Soc. 195 (1974), 305-316
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364554-5
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Abstract:
Let $\mathfrak {N}$ be the maximal nilpotent ideal in a Borel subalgebra of a complex simple Lie algebra. The cohomology groups ${H^1}(\mathfrak {N},\mathfrak {N}),{H^1}(\mathfrak {N},{\mathfrak {N}^\ast })$ and the $\mathfrak {N}$-invariant symmetric bilinear forms on $\mathfrak {N}$ are determined. The main result is the computation of ${H^2}(\mathfrak {N},\mathfrak {N})$.References
- N. Bourbaki, Éléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chapitre IV: Groupes de Coxeter et systèmes de Tits. Chapitre V: Groupes engendrés par des réflexions. Chapitre VI: systèmes de racines, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1337, Hermann, Paris, 1968 (French). MR 0240238
- Bertram Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329–387. MR 142696, DOI 10.2307/1970237
- G. Leger and E. Luks, Cohomology theorems for Borel-like solvable Lie algebras in arbitrary characteristic, Canadian J. Math. 24 (1972), 1019–1026. MR 320104, DOI 10.4153/CJM-1972-103-1 F. Williams, Laplace operators and the $\mathfrak {h}$-module structure of certain cohomology groups (in preparation).
Bibliographic Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 195 (1974), 305-316
- MSC: Primary 22E45; Secondary 22E25
- DOI: https://doi.org/10.1090/S0002-9947-1974-0364554-5
- MathSciNet review: 0364554