The relationship of global dimensions between the H-bimodule algebra A and its twisted smash product A * H is established.
In this paper,we give a sufficient and necessary condition for generalized L-R-smash products or generalized diagonal crossed products to be bialgebras(Hopf algebras),and mainly give a Maschke theorem for L-R-smash products,and hence obtain Maschke theorems for twisted smash products and diagonal crossed products.
On the basis of free product of algebras,the free product of weak Hopf algebras and the free product of(s,i)-bialgebras are investigated in this paper.It is proved that the two free products are also a weak Hopf algebra and an(s,i)-bialgebra,respectively.
