"Quantum Groups and Noncommutative Spaces'', M. Marcolli, D. Parashar (eds.), Vieweg+Teubner Verlag (Max-Planck Series) vol. E41, 2011, 104-120; arXiv:0809.0638.
Mathematics Subject Classification (2000): 16W30, 16W35, 16S35, 16E99, 16R50, 58B32, 58B34, 81R50, 81R60, 16H05, 13B05, 13B22
Abstract. 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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(8 décembre 2010)