When is a cleft extension Azumaya?

Details When is a cleft extension Azumaya? When is a cleft extension Azumaya?

2004-04-21

arxiv.org/abs/math/0404381v1

Mathematics

Rings and Algebras

Scientific paper

We show which $H^{op}$-cleft extensions $k#_\sigma H^{op}$ of the base field $k$ for a dual quasitriangular Hopf algebra $(H, r)$ are $H$-Azumaya. The result is given in terms of bijectivity of a map $\theta_\sigma\colon H\to H^*$ defined in terms of $r$ and the 2-cocycle $\sigma$, generalizing a well-known result for the commutative and cocommutative case. We illustrate the Theorem with an explicit computation for the Hopf algebras of type E(n).

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