We show which H-op-cleft extensions k#H-sigma(op) of k for a dual quasi-triangular Hopf algebra (H, r) are H-Azumaya. The result is given in terms of bijectivity of a map theta(sigma): H -> H* defined in terms of the universal r-form r and the 2-cocycle sigma, generalizing a well-known result for the commutative and co-commutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).
When is a cleft extension H-Azumaya?
CARNOVALE, GIOVANNA
2006
Abstract
We show which H-op-cleft extensions k#H-sigma(op) of k for a dual quasi-triangular Hopf algebra (H, r) are H-Azumaya. The result is given in terms of bijectivity of a map theta(sigma): H -> H* defined in terms of the universal r-form r and the 2-cocycle sigma, generalizing a well-known result for the commutative and co-commutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).
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