Stable Clifford theory

Stable Clifford Theory for Divisorially Graded Rings

Dade [D1, Theorem 7.4] obtained an important result on the equivalence of categories, extending the classical stable Clifford theory. He used the theory of strongly graded rings. Recently, this work has been generalized to arbitrary graded rings, see E. Dade [D2], [D3], J.L. Gómez Pardo and C. Nǎstǎsescu [GN ], C. Nǎstǎsescu and F. Van Oystaeyen [NVO2]. In the classical case the stable Clifford...

Clifford Theory for Cocentral Extensions

The classical Clifford correspondence for normal subgroups is considered in the more general setting of semisimple Hopf algebras. We prove that this correspondence still holds if the extension determined by the normal Hopf subalgebra is cocentral.

Clifford Theory for Association Schemes

Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset coniatns conjugate characters with same multiplicities. Moreover some strong relations are obtained.

Clifford theory for tensor categories

A graded tensor category over a group G will be called a strongly G-graded tensor category if every homogeneous component has at least one invertible object. Our main result is a description of the module categories over a strongly G-graded tensor category as induced from module categories over tensor subcategories associated with the subgroups of G.

On Clifford Theory of Vertex Operator Algebras