Let H be a Hopf algebra over a field k and A/B a right H-Galois extension. Then in this note a spectral sequence for Ext will be constructed which yields the estimate for global dimension of A in terms of the corresponding data for H and B. As an application, we obtain the Maschke-type theorems for crossed products and twisted smash products. Finally, the relationship of finitistic dimensions between A and B will be given, if H is semisimple.
LIU, LING and GUO, QIAOLING
"Global and finitistic dimension of Hopf-Galois extensions,"
Turkish Journal of Mathematics: Vol. 37:
2, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss2/3