Hopf代数的双交叉积

The Bicrossed Products of Hopf Algebras

本文定义并详细讨论了交叉余积，考虑交叉积与交叉余积合起未成为双代数的问题，讨论了由内作用，内余作用构造的双交叉积．我们还用正合序列刻划了双交叉积．

The purpose of this paper is to begin to lay the foundation of bicrossed products of Hopf algebra. The theory is motivated by asking that crossed product and crossed coproduct fit together to form a bialgebra. It is the further generalization of bismash product of Hopf algebra. We investigate the basic properties of these notions and give the exact sequence characterization of bicrossed product. We will see that any bicrossed product H with weakly inner action and inner coaction is isomorphic to a bicrossed product H A with trivial action ' and trivial coactionβ'.