Weyl type algebras from quantum tori
文献类型：期刊论文
| 作者 | Zhao, KM |
| 刊名 | COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
 |
| 出版日期 | 2006-04-01 |
| 卷号 | 8期号:2页码:135-165 |
| 关键词 | quantum torus simple associative algebra derivation second cohomology group isomorphism |
| ISSN号 | 0219-1997 |
| 英文摘要 | We introduce and study the quantum version of the differential operator algebra on Laurent polynomials and its associated Lie algebra over a field F of characteristic 0. The q-quantum torus F-q is the unital associative algebra over F generated by t(1)(+/- 1),...,t(n)(+/- 1) subject to the defining relations t(i)t(j) = q(i), (j)t(j)t(i), where q(i,i) = 1, q(i,j) = q(j,i)(-1). Let D be a subspace of circle plus(n)(i=1) F partial derivative(i) where partial derivative(i) is the derivation of F-q sending t(i)(k1...)t(n)(kn) to k(i)t(1)(...)(k1)t(n)(kn). Then, the quantum differential operator algebra is the associative algebra F-q[D]. Assume that F-q[D] is simple as an associative algebra. We compute explicitly all 2-cocycles of F-q[D], viewed as a Lie algebra. More precisely, we show that the second cohomology group of F-q[D] has dimension n if D = 0, dimension 1 if dim D = 1, and dimension 0 if dim > 1. We also determine all isomorphisms and anti-isomorphisms F-q[D] -> F-q'[D'] of simple associative algebras, and all isomorphisms F-q[D]/F -> F-q'[D']/F of simple Lie algebras. |
| 语种 | 英语 |
| WOS记录号 | WOS:000237496200001 |
| 出版者 | WORLD SCIENTIFIC PUBL CO PTE LTD |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/3650]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Zhao, KM |
| 作者单位 | 1.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Zhao, KM. Weyl type algebras from quantum tori[J]. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,2006,8(2):135-165. |
| APA | Zhao, KM.(2006).Weyl type algebras from quantum tori.COMMUNICATIONS IN CONTEMPORARY MATHEMATICS,8(2),135-165. |
| MLA | Zhao, KM."Weyl type algebras from quantum tori".COMMUNICATIONS IN CONTEMPORARY MATHEMATICS 8.2(2006):135-165. |
入库方式： OAI收割
来源：数学与系统科学研究院
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