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Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras. (English) Zbl 0703.17016

The aim of this paper is to prove the existence of the strong Bernstein- Gel’fand-Gel’fand (BGG) resolution for arbitrary Kac-Moody algebras, known up to now for the symmetrizable case [I. N. Bernstein, I. M. Gel’fand and S. I. Gel’fand, Lie groups Represent., Proc. Summer Sch. Bolyai János Math. Soc., Budapest 1971, 21-64 (1975; Zbl 0338.58019); H. Garland and J. Lepowsky, Invent. Math. 34, 37- 76 (1976; Zbl 0358.17015); G. Kempf, Adv. Math. 29, 310-396 (1978; Zbl 0393.20027)]. Some standard consequences of the BGG resolution are given. In particular, the author obtains Konstant’s theorem on “\({\mathfrak n}\)-homology” for arbitrary Kac-Moody algebras (known so far only in the symmetrizable case).
Reviewer: J.Kubarski

MSC:

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

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