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On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras

I. Heckenberger·S. Kolb
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Abstract

A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-Gelfand resolution for symmetrizable Kac-Moody algebras are established. For quantized enveloping algebras with fixed complex nonzero deformation parameter q exactness is proven for all q which are not a root of unity.

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I. Heckenberger, S. Kolb. 2006-05-17. On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras. https://arxiv.org/abs/math/0605460

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