In this paper, the concepts of a weak Hopf algebra and a quasi-braided almost bialgebra are introduced. It is shown that the quantum quasi-doubles of some weak Hopf algebras are quasi-braided almost bialgebras. This fact implies that some new solutions of the quantum Yang-Baxter equation can be constructed from some weak Hopf algebras, in particular, when the weak Hopf algebra is a finite Clifford monoid algebra.

In this paper, a su cient condition is given under which the smash product A#H is a trans nite left free normalizing extension of an algebra A. Moreover, the result is applied to a skew semigroup ring, a skew group ring and the quantum group Uq(sl(2)) such that some properties are shown.

本文在余代数上定义了五类等价关系，它们是Green等价g，D，L，R，H。然后给出了这些等价关系一些基本性质和结构特点。在每个Green等价的等价类集上构造了一种偏序并给出了偏序上半格和结构的刻划。用g-，L-，R-类分别出了子余代数、左余理想、右余理想的结构刻划。进一步地，本文研究了张量积上的Green等价划及余代数同态的Green保持性和提升性。作为应用，本文得到了两个不可约余代数的张量积仍为不可约余代数的一人重要条件；证明了不可约余、代数在g-保持余代数同态下的同态像是不可约的。