量子交换余模代数与相对Hopf模范畴  

Quantum Commutative Comodule Algebras and Categories of Relative Hopf Modules

作　　者：胡国权[1] 

机构地区：[1]湖南师范大学数学系

出　　处：《湖南师范大学自然科学学报》1996年第1期13-16,共4页Journal of Natural Science of Hunan Normal University

基　　金：国家自然科学基金

摘　　要：拟三角Ｈｏｐｆ代数Ｈ的（左）模范畴ＨＭ与辫化Ｈｏｐｆ代数Ｈ＇的（右）余模范畴ＭＨ＇都是辫化单式范畴，考虑其中的量子交换代数Ａ，Ｍ．Ｃｏｈｅｎ等证明相应Ｓｍａｓｈ积代数Ａ＃Ｈ的模范畴Ａ＃ＨＭ是一个单式范畴．本文考虑一种对偶情形，设Ａ是Ｈ＇－交换代数，则（Ａ，Ｈ＇）－Ｈｏｐｆ模范畴是单式范畴．The category H_M of (left) modules over a quasitriangular Hopf algebra H and the category M￣H' of (right) H'-comodules over a braided Hopf algebra H' are typical examples of braided monoidal categories. M. Cohen et al. showed that the category (A#H)_M of (left) modules over the smash product algebra A # H associated to a quantum commutative algebra A in H_M is monoidal. we examine a dual situation, that is, a quantum commutativealgebra A in M￣H', and show that the category of relative [A, H']-Hopf modules is monoidal.

关 键 词：单式范畴 相对郝普夫模 量子交换模代数 

分 类 号：O153.3[理学—数学] O154[理学—基础数学]