A Note on Finitistic Dimension of Hopf-Galois Extensions

Let H be a finite-dimensional Hopf algebra over a field k and A/B be a right H-Galois extension. If the functors A ⊗ B  − and B (−) are both separable, then the finitistic dimension of A is equal to that of B.

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Bibliographic Details
Published in:Communications in algebra 2014-01, Vol.42 (10), p.4392-4395
Main Authors: Shen, Bing-liang, Zhou, Xuan
Format: Article
Language:English
Subjects:
Algebra
Finitistic dimension
Hopf-Galois extension
Separable functor
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Summary:Let H be a finite-dimensional Hopf algebra over a field k and A/B be a right H-Galois extension. If the functors A ⊗ B  − and B (−) are both separable, then the finitistic dimension of A is equal to that of B.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.811514