Let H be a Hopf algebra. A unital H-comodule algebra is called homogeneous if the algebra of coinvariants equals the ground field. A (not necessarily unital) H-comodule algebra is called Galois, or principal, or free, if the canonical map, also known as the Galois map, is bijective. In this paper, we establish a duality between a particular class of homogeneous H-comodule algebras, up to H-Morita equivalence, and a particular class of Galois H-comodule algebras, up to H-comodule algebra isomorphism.

中文翻译：

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Hopf代数的同质和Galois相互作用的对应关系。

令H为Hopf代数。如果协变的代数等于地场，则单位H -comodule代数称为齐次。如果规范图（也称为伽罗瓦图）是双射的，则一个（不一定是整体的）H协模代数称为Galois或本金或自由。在本文中，我们在直到H -Morita等价的一类齐次H-协模代数和直到H -comodule代数同构的一类Galois H-协模代数之间建立对偶性。