Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras

Details Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras

2004-10-11

arxiv.org/abs/math/0410263v2

Mathematics

Quantum Algebra

Reference to Schauenburg's work is added. Section 4 is improved using a Kac-Schauenburg-type exact sequence

Scientific paper

We propose a detailed systematic study of a group H^2_L(A) associated, by elementary means of lazy 2-cocycles, to any Hopf algebra A. This group was introduced by Schauenburg (with a different name) in order to generalize G.I. Kac's exact sequence. We study the various interplays of lazy cohomology in Hopf algebra theory: Galois and biGalois objects, Brauer groups and projective representations. We obtain a Kac-Schauenburg-type sequence for double crossed products of possibly infinite-dimensional Hopf algebras. Finally the explicit computation of H^2_L(A) for monomial Hopf algebras and for a class of cotriangular Hopf algebras is performed.

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