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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cohomology of nilradicals of Borel subalgebras

Authors: George F. Leger and Eugene M. Luks
Journal: Trans. Amer. Math. Soc. 195 (1974), 305-316
MSC: Primary 22E45; Secondary 22E25
MathSciNet review: 0364554
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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 [Enhancements On Off] (What's this?)

  • [1] N. Bourbaki, Eléments de mathématique. Fasc. XXXIV. Groupes et algèbres de Lie. Chap. IV: Groupes de Coxeter et systèmes de Tits. Chap. V: Groupes engendrés par des réflexions. Chap. VI: Systèmes de racines, Actualités Sci. Indust., no. 1337, Hermann, Paris, 1968. MR 39 #1590. MR 0240238 (39:1590)
  • [2] B. Kostant, Lie algebra cohomology and the generalized Borel-Weil theorem, Ann. of Math. (2) 74 (1961), 329-387. MR 26 #265. MR 0142696 (26:265)
  • [3] G. Leger and E. Luks, Cohomology theorems for Borel-like solvable Lie algebras in arbitrary characteristic, Canad. J. Math. 24 (1972), 1019-1026. MR 0320104 (47:8645)
  • [4] F. Williams, Laplace operators and the $ \mathfrak{h}$-module structure of certain cohomology groups (in preparation).

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