Abelian and non-abelian second cohomologies of quantized enveloping algebras

Details Abelian and non-abelian second cohomologies of quantized enveloping algebras Abelian and non-abelian second cohomologies of quantized enveloping algebras

2007-08-15

arxiv.org/abs/0708.1982v4

Mathematics

Quantum Algebra

40 Pages, the final version to appear in J. Algebra; mainly, typos corrected

Scientific paper

For a class of pointed Hopf algebras including the quantized enveloping algebras, we discuss cleft extensions, cocycle deformations and the second cohomology. We present such a non-standard method of computing the abelian second cohomology that derives information from the non-abelian second cohomology classifying cleft extensions. As a sample computation, a quantum analogue of Whitehead's second lemma for Lie-algebra cohomology is proved.

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