弱Hopf代数与正则幺半群

本文定义了弱Ｈｏｐｆ代数并研究了弱Ｈｏｐｆ代数的弱对极与类群元幺半群的关系．首先，本文给出弱Ｈｏｐｆ代数的一些基本性质；然后，对类群元幺半群是逆半群或纯正半群的某些弱Ｈｏｐｆ代数，描述了其弱对极的一些性质；最后，给出一类其类群元幺半群为正则半群的弱Ｈｏｐｆ代数．

Weak Hopf Algebras and Regular Monoids

Weak Hopf algebra is defined. The aim of this work is to study the relations between the weak antipode of a weak Hopf algelra and the monoid of group like elements. At first, the author shows some properties of weak Hopf algebras. And, for some weak Hopf algebras, some properties of the weak antipodes are given if the monoids of group like elements are inverse or orthodox semigroups. At end, the author gets a weak Hopf algebra whose monoid of group like elements is regular.