Abstract
In this chapter we prove two rigidity theorems, both needed in Chapter XIX. The first one is classical: it asserts that any formal deformation of the enveloping algebra of a semisimple Lie algebra is trivial. The proof is based on the vanishing of certain cohomology groups. The second rigidity result is due to Drinfeld [Dri89b] [Dri90]. It states that if A and A’ are quantum en-veloping algebras with the same underlying cocommutative bialgebras and the same universal R-matrices, then there exists a gauge transformation from A to A’. The proof again relies on some cohomological considerations, this time involving the cobar complex of a symmetric coalgebra.
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© 1995 Springer Science+Business Media New York
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Kassel, C. (1995). Cohomology and Rigidity Theorems. In: Quantum Groups. Graduate Texts in Mathematics, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0783-2_18
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DOI: https://doi.org/10.1007/978-1-4612-0783-2_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6900-7
Online ISBN: 978-1-4612-0783-2
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