Smash积代数和量子模范畴中的Hopf代数的新对偶  

THE NEW DUALITIES OF SMASH PRODUCT ALGEBRAS AND HOPF ALGEBRAS IN THE CATEGORY OF YETTER-DRINFEL'D MODULES

作　　者：张良云[1] 陈惠香[2] 

机构地区：[1]南京农业大学理学院,南京210095 [2]扬州大学数学系,江苏扬州225002

出　　处：《数学年刊（A辑）》2003年第4期473-482,共10页Chinese Annals of Mathematics

基　　金：国家自然科学基金;南京农业大学优秀博士基金

摘　　要：本文引入模代数的一种新对偶,它推广了代数的有限对偶概念,并证明:通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)~0 _HA^0×H^0余代数同构,最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的。This paper introduces a notion of the new dual of module algebras, which generalizes the notion of the finite dual of algebras. It is proved that the dual of a module algebra is a comdule coalgebra via the dual function. Hence a smash coproduct is constructed. Moveover, it is proved that the dual of a smash product is a smash coproduct, that is, there exists a coalgebra isomorphism: (A#H)0 = HA0 × H0. Finally, it is proved that bialgebras (Hopf algebras) in the category YD(H) of left H-Yetter-Drinfel'd modules are self-dual via the dual function.

关 键 词：HOPF代数 模代数 SMASH积 量子模 

分 类 号：O153.3[理学—数学]