Research on quantum matrices and Hopf algebras

量子矩阵和Hopf代数研究

• 批准号: 11640007
• 负责人: MITSUSHIRO Takeuchi
• 金额: $ 2.24万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640007/
• 关键词: quantum matrix; quantum group; Hopf algebra; braid; modular category; braided category; biFrobenius algebra; cylinder matrix; Homfly多項式; ボゾン化; コホモロジー; ヘッケ代数; matched pair; Kaplansky予想; Kac-Moody群; 頂点作用素代数; braided category; braidedホップ代数 /

The principal investigator has studied quantum matrices and Hopf algebras related to quantum groups and obtained the following results. 1.Results on finite Hopf algebras in braided categories including Hopf modules and integrals appear in J. Pure and Appl. Algebra. 2. New concepts of cylinder matrix and cylinder algebra are investigated as variation of quantum matrices and the results appear in J. Algebra. 3. New concept of biFrobenius algebra arises from a joint work with Doi and its basic properties and the braid version appear in Contemp. Math.. 4. Modular categories and Hopf algebras are studied from a new point of view and an elementary proof of Etingof and Gelaki's theorem on dimension of irreducible modules is obtained and appears in J. Algebra. 5. Survey on quantum matrices with emphasis on braid theory, quantized linear algebra, Homfly polynomial, Hecke algebra and q-Schur algebra, cocycle deformation appears in MSRI Publ.. 6. ESS-LYZ theory on matched pairs of groups is studied from a new point of view and some new results are obtained. 7. Radford-Majid bosonization is studied from a new point of view.

主要研究者研究了与量子群相关的量子矩阵和Hopf代数，并得到了以下结果。 1.编织类别中的有限 Hopf 代数（包括 Hopf 模和积分）的结果出现在 J. Pure 和 Appl 中。代数。 2. 作为量子矩阵的变分，研究了圆柱矩阵和圆柱代数的新概念，结果发表在《J. Algebra》上。 3. biFrobenius代数的新概念源于与Doi的联合工作，其基本性质和辫子版本出现在Contemp中。数学.. 4.从新的角度研究模范畴和Hopf代数，得到Etingof和Gelaki不可约模维数定理的基本证明，并发表在J. Algebra中。 5. 量子矩阵综述，重点是辫子理论、量化线性代数、Homfly 多项式、Hecke 代数和 q-Schur 代数，余循环变形出现在 MSRI 出版物中。 6. 从一个角度研究了配对群的 ESS-LYZ 理论取得了一些新的观点和新的成果。 7.从新的角度研究Radford-Majid玻色化。

项目成果

M.Takeuchi: "A short course on quantum matrices"Math.Sci.Res.Inst.Publications. 43. 383-435 (2002)

M.Takeuchi：“量子矩阵短期课程”Math.Sci.Res.Inst.Publications。

M. Miyamoto: "3-state Potts model and automorphisms"J. Algebra. 239. 56-76 (2001)

M. Miyamoto：“三态 Potts 模型和自同构”J。

Y.Egama and M.Miyamoto: "Graph labelings in Boolean lattices"Ars Combin.. 52. 13-19 (1999)

Y.Egama 和 M.Miyamoto：“布尔格中的图形标签”Ars Combin.. 52. 13-19 (1999)

A.Masuoka: "Cohomology and coquasi-bialgebra extensions"Adv.Math.. 173. 262-315 (2003)

A.Masuoka：“上同调和 coquasi-bialgebra 扩展”Adv.Math.. 173. 262-315 (2003)

M.Takeuchi: "Survey of braided Hopf algebras"Contemporary Mathematics. 267. 301-323 (2000)

M.Takeuchi：《辫状Hopf代数综述》当代数学。