Mathematics – Quantum Algebra
Scientific paper
2008-09-03
Proceedings of the Workshop on Quantum Groups and Noncommutative Geometry, M. Marcolli and D. Parashar (eds.), MPIM, Bonn 2007
Mathematics
Quantum Algebra
17 pages. Small changes in introduction and additional references
Scientific paper
In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension A(H,c) to each twisted algebra H(c) obtained from a Hopf algebra H by twisting its product with the help of a cocycle c. The algebra A(H,c) is a flat deformation of H(c) over a "big" central subalgebra B(H,c) and can be viewed as the noncommutative analogue of a versal torsor in the sense of Serre. After surveying the results on A(H,c) obtained with Aljadeff, we establish three new results: we present a systematic method to construct elements of the commutative algebra B(H,c), we show that a certain important integrality condition is satisfied by all finite-dimensional Hopf algebras generated by grouplike and skew-primitive elements, and we compute B(H,c) in the case where H is the Hopf algebra of a cyclic group.
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