Hopf Group Algebra And Its Yetter - Drinfeld Model Domain

This dissertation consists of five sections. We shall investigate Hopf group algebraand it’s Yetter-Drinfeld module of Hopf group algebra and their applications, and last weshow some corresponding examples, concluded five sections.The first sections are introduction and preliminaries.The second section we introduce the Hopf group algebra and give some propeties andsome other difinition.In the third section, we study the Yetter-Drinfled module with one corssed structureand give some examples and prove it to be a braided Turaev group category it to a braidedTuraev category. then we also introduce the difinition such asHY DH,HY DH, Y DHIn the forth section, we continue to study Yetter-Dinfeld mldule with two crossedstructure,then give the difinitions such asHY DH,and thenIn the fifth section, we give some applications of Yetter-Drinfeld module we provedtheorem5.2and theorem5.3.