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

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

2006-05-17

arxiv.org/abs/math/0605460v1

Mathematics

Quantum Algebra

12 pages

Scientific paper

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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