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

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

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Authors and Affiliations

  1. Mathematisches Institut, Universitat Leipzig, Augustusplatz 10-11, 04109 Leipzig, Germany

    I. Heckenberger

  2. Mathematics Department, Virginia Polytechnic Institute and State University , Blacksburg, VA 24061, USA

    S. Kolb

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  1. I. Heckenberger
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  2. S. Kolb
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Correspondence to I. Heckenberger or S. Kolb.

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Heckenberger, I., Kolb, S. On the Bernstein-Gelfand-Gelfand Resolution for Kac-Moody Algebras and Quantized Enveloping Algebras. Transformation Groups 12, 647–655 (2007). https://doi.org/10.1007/s00031-007-0059-2

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  • DOI: https://doi.org/10.1007/s00031-007-0059-2

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