Generalized quantum groups, including super and elliptic ones, and Weyl groupoids

广义量子群，包括超群和椭圆群，以及韦尔群群

• 批准号: 19540027
• 负责人: YAMANE Hiroyuki
• 金额: $ 1.83万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2009
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19540027/
• 关键词: ワイル亜群; ニコルス代数; 量子群; スーパー代数; ホップ代数; 無限次元Lie代数; スーパーLie代数; Nichols代数

In 2006, Yamane, with Heckenberger, introduced axioms of Weyl groupoids and showed that Weyl groupoids satisfy a Matsumoto-type theorem. In 2008, using this result, they gave a factorization formula for the Shapovalov determinants of generalized quantum groups, including quantum superalgebras, by using the longest elements of the Weyl groupoids. This study is epoch-making since it was achieved by using intensively a special situation happened at roots of unity. Under some special conditions, simlar theorems were shown by several people, but their proofs were made by using the Shapovalov's original result for the simple Lie algebras.

2006年，Yamane与Heckenberger一起引入了Weyl类的公理，并表明Weyl-clastoids满足了松本型定理。在2008年，使用此结果，它们通过使用Weyl groupoids的最长元素来为广义量子基团的沙波瓦洛夫决定因素（包括量子超级对桥）的决定因素提供了分解公式。这项研究是划时的，因为它是通过强烈的统一根源发生特殊情况而实现的。在某些特殊条件下，几个人显示了Simlar定理，但是它们的证明是通过使用Shapovalov的原始结果来进行简单的代数来做出的。

项目成果

Recent progress on Drinfeld doubles and BDFG-type Lie tori

德林菲尔德双打和 BDFG 型李托里的最新进展

• 发表时间: 2009
• 作者: aeid Azam;Hiroyuki Yamane;Malihe Yousofzader;Hiroyuki Yamane
• 通讯作者: Hiroyuki Yamane

Heckenberger' s Lusztig-type isomorphisms and Shapovalov determinants of quantum doubles of finite type

有限型量子双打的 Heckenberger 的 Lusztig 型同构和 Shapovalov 行列式

• 发表时间: 2008
• 作者: aeid Azam;Hiroyuki Yamane;Malihe Yousofzader;Hiroyuki Yamane;Hiroyuki Yamane;H. Yamane;Masao Ishikawa and Jiang Zeng;山根宏之
• 通讯作者: 山根宏之

On Coxeter groupoids and their Iwahori-Hecke type algebras

关于 Coxeter 群群及其 Iwahori-Hecke 型代数

• 发表时间: 2008
• 作者: aeid Azam;Hiroyuki Yamane;Malihe Yousofzader;Hiroyuki Yamane;Hiroyuki Yamane;H. Yamane;Masao Ishikawa and Jiang Zeng;山根宏之;Masao Ishikawa;山根宏之;H. Yamane;M. Ishikawa;H. Yamane
• 通讯作者: H. Yamane

Shapovalov determinants of Drinfel'd double

Drinfeld 双精度的 Shapovalov 决定因素

• 发表时间: 2008
• 作者: aeid Azam;Hiroyuki Yamane;Malihe Yousofzader;Hiroyuki Yamane;Hiroyuki Yamane;H. Yamane;Masao Ishikawa and Jiang Zeng;山根宏之;Masao Ishikawa;山根宏之
• 通讯作者: 山根宏之

Calculation of the multiplicity of the null roots of elliptic Lie algebras

椭圆李代数零根重数的计算

• 发表时间: 2008
• 作者: aeid Azam;Hiroyuki Yamane;Malihe Yousofzader;Hiroyuki Yamane;Hiroyuki Yamane;H. Yamane
• 通讯作者: H. Yamane