Hopf algebras, operators and combinatorics

Hopf 代数、运算符和组合数学

• 批准号: 371994-2009
• 负责人: Mastnak, Mitja
• 金额: $ 1.38万
• 依托单位: Saint Mary's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=503664
• 关键词: Hopf; algebras; operators; combinatorics

I am most interested in problems involving interplay between several branches of mathematics. There is an abundance of such problems involving Hopf algebras; these are algebraic structures arising in numerous parts of mathematics, as well as in physics. Examples of Hopf algebras include group algebras, universal envelopes of Lie algebras, algebras of representative functions on Lie groups, coordinate algebras of algebraic groups, and quantum groups.

我最感兴趣的问题涉及数学的几个分支之间的相互作用。 有丰富的此类问题涉及霍普夫代数;这些都是代数结构中出现的许多部分的数学，以及在物理学。 Hopf代数的例子包括群代数、李代数的泛包络、李群上的代表函数的代数、代数群的坐标代数和量子群。