Transformation Groups

, Volume 12, Issue 4, pp 647–655

On the Bernstein-Gelfand-Gelfand Resolution for Kac-Moody Algebras and Quantized Enveloping Algebras


DOI: 10.1007/s00031-007-0059-2

Cite this article as:
Heckenberger, I. & Kolb, S. Transformation Groups (2007) 12: 647. doi:10.1007/s00031-007-0059-2


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 deformation parameter \(q\in {\Bbb C}\backslash\{0\}\) exactness is proven for all q which are not a root of unity.

Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

  1. 1.Mathematisches Institut, Universitat Leipzig, Augustusplatz 10-1104109 LeipzigGermany
  2. 2.Mathematics Department, Virginia Polytechnic Institute and State University Blacksburg, VA 24061USA