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The basic construction from the conditional expectation on the quantum double of a finite group

Qiaoling Xin, Lining Jiang, Zhenhua Ma (2015)

Czechoslovak Mathematical Journal

Let G be a finite group and H a subgroup. Denote by D ( G ; H ) (or D ( G ) ) the crossed product of C ( G ) and H (or G ) with respect to the adjoint action of the latter on the former. Consider the algebra D ( G ) , e generated by D ( G ) and e , where we regard E as an idempotent operator e on D ( G ) for a certain conditional expectation E of D ( G ) onto D ( G ; H ) . Let us call D ( G ) , e the basic construction from the conditional expectation E : D ( G ) D ( G ; H ) . The paper constructs a crossed product algebra C ( G / H × G ) G , and proves that there is an algebra isomorphism between D ( G ) , e and C ( G / H × G ) G .

The geometric reductivity of the quantum group S L q ( 2 )

Michał Kępa, Andrzej Tyc (2011)

Colloquium Mathematicae

We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants A G is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...

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