Hopf-Galois theoretic approach to quantum groups

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Hopf-Galois extensions of non-commutative algebras are a non-commutative analogue of principal homogeneous spaces(or torsors)in algebraic geometry, and of principal fiber bundles in algebraic topology. Ideas and techniques developed in Hopf-Galois theory can be effectively applied to study non-commutative or super-commutative algebras, and descent theory as well. The investigator did apply these to study quantum groups, algebraic super-groups and Picard-Vessiot theory. The obtained results include the construction of a series of Hopf algebras including the quantized enveloping algebras, by using cocycle deformation, together with its applications to study of generalized q-boson algebras and generalized quantum doubles.