Quantum Groups pp 420-448 | Cite as

Cohomology and Rigidity Theorems

  • Christian Kassel
Part of the Graduate Texts in Mathematics book series (GTM, volume 155)


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.


Gauge Transformation Topological Algebra Rigidity Theorem Free Left Dual Vector Space 
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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Christian Kassel
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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