On the Hopf Schur group of a field

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• Ehud Meir (Newton Institute)
• Wednesday 02 March 2011, 16:30-17:30
• MR15.

If you have a question about this talk, please contact Christopher Brookes.

Let k be a field. We ask what k-central simple algebras can we get as quotients of Hopf algebras. We call the corresponding subgroup of Br(k) the Hopf Schur group of k. This generalizes the question of what central simple k-algebras are quotients of group algebras (the so called Schur algebras) and the Schur subgroup of Br(k). Since group algebras are Hopf algebras, every Schur algebra is a Hopf Schur algebra. The Schur subgroup might be a very small subgroup of Br(k), and we ask what other Hopf Schur algebras can we find.

In this talk I will try to explain why actually every k-central simple algebra is a Hopf Schur algebra up to Brauer equivalence. We shall do so by giving a representation theoretic definition of Hopf algebras, and by considering forms of Hopf algebras. All the relevant notions will be explained.

This talk is part of the Algebra and Representation Theory Seminar series.

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