Examines affine commutative-by-finite Hopf algebras over algebraically closed fields, deriving bounds on simple module dimensions and structural constraints when the finite extension is semisimple and cosemisimple.
O_e(G) is a free module over O(G)
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abstract
We show that the quantised function algebra O_e(G) of a simply-connected semisimple algebraic group G at a root of unity is a free module over the subring isomorphic to O(G).
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Affine commutative-by-finite Hopf algebras
Examines affine commutative-by-finite Hopf algebras over algebraically closed fields, deriving bounds on simple module dimensions and structural constraints when the finite extension is semisimple and cosemisimple.