Dynamical Yang-Baxter maps and Hopf algebroids

Research Project

Project/Area Number	22540001
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Algebra
Research Institution	Hokkaido University
Principal Investigator	SHIBUKAWA Youichi 北海道大学, 理学(系)研究科(研究院), 准教授 (90241299)
Project Period (FY)	2010-10-20 – 2014-03-31
Project Status	Completed (Fiscal Year 2013)
Budget Amount *help	¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000) Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords	ダイナミカル・ヤン・バクスター写像 / ホップ亜代数 / リジッドなテンソル圏 / テンソル圏 / 双対 / ブレイテッド・モノイド / 等質空間 / 面代数
Research Abstract	The main result of this research is to construct algebras, such as Hopf algebroids and face algebras, from dynamical Yang-Baxter maps, solutions to a version of the quantum dynamical Yang-Baxter equation. By making use of these Hopf algebroids, we provided with rigid tensor categories, which are tensor categories with "duals". In addition, we established a method to produce the dynamical Yang-Baxter map.