Affiliation:
1. Nanjing Agricultural University, College of Science, Nanjing, Jiangsu, P.R. of China
Abstract
Let H be a finite dimensional weak Hopf algebra and A/B be a right faithfully
flat weak H-Galois extension. Then in this note, we first show that if H is
semisimple, then the finitistic dimension of A is less than or equal to that
of B. Furthermore, using duality theorem, we obtain that if H and its dual
H* are both semisimple, then the finitistic dimension of A is equal to that
of B, which means the finitistic dimension conjecture holds for A if and
only if it holds for B. Finally, as applications, we obtain these relations
for the weak crossed products and weak smash products.
Publisher
National Library of Serbia