| Verlinde模性范畴上的Casimir数及其应用 |
| |
| 引用本文： | 王志华,李立斌.Verlinde模性范畴上的Casimir数及其应用[J].数学学报,2018,61(1):59-66. |
| |
| 作者姓名： | 王志华 李立斌 |
| |
| 作者单位： | 1. 泰州学院数理学院 泰州 225300;
2. 南京大学数学系 南京 210009;
3. 扬州大学数学科学学院 扬州 225002 |
| |
| 基金项目： | 国家自然科学基金资助项目（11471282）；中国博士后科学基金资助项目（2017M610316） |
| |
| 摘 要： | 本文计算了秩为n+1的一类特殊的Verlinde模性范畴L的Casimir数,计算结果表明该Casimir数为2n+4.作为应用,由Higman定理知域K上的Grothendieck代数Gr(L)_Z K是半单代数当且仅当2n+4在域K中不为零.这也给出了第二类型n+1次Dickson多项式E_(n+1)(X)在KX]中无重因式的一个等价刻画.如果2n+4在域K中为零,借助于Dickson多项式的有关因式分解定理,本文完全给出了Grothendieck代数Gr(L)_Z K的Jacobson根.
|
| 关 键 词： | Grothendieck环 Verlinde模性范畴 Casimir数 Jacobson根 Dickson多项式 |
The Casimir Number of a Verlinde Modular Category and Its Applications |
| |
| Zhi Hua WANG,Li Bin LI.The Casimir Number of a Verlinde Modular Category and Its Applications[J].Acta Mathematica Sinica,2018,61(1):59-66. |
| |
| Authors: | Zhi Hua WANG Li Bin LI |
| |
| Institution: | 1. Department of Mathematical Sciences, Taizhou College, Taizhou 225300, P. R. China;
2. Department of Mathematics, Nanjing University, Nanjing 210009, P. R. China;
3. School of Mathematical Science, Yangzhou University, Yangzhou 225002, P. R. China |
| |
| Abstract: | In this paper the Casimir number of a special kind of Verlinde modular category l of rank n+1 is calculated to be 2n+4. As an application it follows from Higman's theorem that the Grothendieck algebra Gr(l) ?Z K over a field K is semisimple if and only if 2n+4 is a unit in K. This is equivalent to saying that the (n+1)-th Dickson polynomial En+1(X) of the second kind has no multiple factors in KX]. If 2n+4 is zero in K, we use the factorizations of Dickson polynomials to describe the Jacobson radical of Gr(l) ?Z K explicitly. |
| |
| Keywords: | Grothendieck ring Verlinde modular category Casimir number Jacobson radical Dickson polynomial |
| 本文献已被 CNKI 等数据库收录！ |
| 点击此处可从《数学学报》浏览原始摘要信息 |
| 点击此处可从《数学学报》下载免费的PDF全文 |
