A Note on Finitistic Dimension of Hopf-Galois Extensions

Abstract

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.

Key Words:

• Finitistic dimension
• Hopf–Galois extension
• Separable functor

2010 Mathematics Subject Classification:

• 16S40
• 16E10

ACKNOWLEDGMENTS

The authors sincerely thank the referee for his or her valuable suggestions and comments. This work is supported by the Foundation of Zhejiang Educational Committee (Y201121955).

Notes

Communicated by K. Misra.