Classification of coquasi-Hopf algebras by tensor equivalence and constructions of new braidings

通过张量等价对 coquasi-Hopf 代数进行分类和新编织的构造

• 批准号: 14540007
• 负责人: MASUOKA Akira
• 金额: $ 1.15万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540007/
• 关键词: Hopf algebra; super-Hopf algebra; super-affine group; group cohomology; II_1 subfactor; Picard-Vessiot theory; Tanaka duality; 淡中双対定理; ホモロジー代数; ホップ・ガロア拡大; 部分因子環; 群のコホモロジー

In what is called "Algebraic Groups" some kinds of objects are involved. The most generalized are affine group (schemes), or representable group-functors on the category of commutative algebras, which are necessarily represented by commutative Hopf algebras. A linearly algebraic group is precisely the group of rational points in a field of such an affine group whose representative Hopf algebra is supposed to be finitely generated. By replacing linear algebraic groups with the generalized object, affine groups or Hopf algebras, we can often remove assumptions such as finite generation, zero characteristic or algebraic closedness. By extending to non-commutative Hopf algebras, we reach the notion of quantum groups. Our team has investigated affine groups, super-affine groups and Hopf-Galois extensions (or non-commutative principal homogeneous spaces) from the view-point of non-commutative algebra and geometry.

在所谓的“代数群”中，涉及到一些类型的对象。最广义的是可交换代数范畴上的仿射群（方案）或可表示群函子，它们必然由可交换Hopf代数表示。线性代数群就是这样一个仿射群的域上的有理点的群，其代表的Hopf代数是有限生成的。通过用广义对象、仿射群或Hopf代数代替线性代数群，我们通常可以消除有限生成、零特征或代数闭性等假设。通过推广到非交换Hopf代数，我们得到了量子群的概念。本小组从非交换代数和几何的角度研究了仿射群、超仿射群和Hopf-Galois扩展（或非交换主齐次空间）。

项目成果

A.Masuoka: "More homological approach to composition of subfactors"Journal of Mathematical Science, University of Tokyo. (掲載予定).

A.Masuoka：“子因子组合的更多同源方法”，东京大学数学科学杂志（待出版）。

A.Masuoka: "Example of almost commutative Hopf algebras which are not coquasitriangular"Dekker, Lec.Notes in Pure and Appl.Math.237. (掲載予定).

A.Masuoka：“非共拟三角的几乎交换的 Hopf 代数的示例”Dekker，Lec.Pure 和 Appl.Math.237 中的注释（待出版）。

A.Masuoka, T.Oka: "Unipotent algebraic affine supergroups and nilpotent Lie superalgebras"Algebras and Representation Theory. (掲載予定).

A.Masuoka，T.Oka：“单能代数仿射超群和幂零李超代数”代数和表示理论（即将出版）。

A.Masuoka: "Hopf algebra extensions and cohomology"MSRI Publications (Cambridge Univ.Press). 43巻. 167-209 (2002)

A.Masuoka：“Hopf 代数扩展和上同调”MSRI Publications（剑桥大学出版社）43. 167-209 (2002)。

A.Masuoka, T.Yanai: "Hopf module duality applied to X-outer Galois theory"Journal of Algebra. (掲載予定).

A.Masuoka，T.Yanai：“Hopf 模对偶性应用于 X-外伽罗瓦理论”代数杂志（待出版）。