Mathematical Sciences: Actions of Finite Groups and Finite Dimensional Hopf Algebras on Rings

数学科学：有限群和有限维霍普夫代数在环上的作用

• 批准号: 9618521
• 负责人: Martin Lorenz
• 金额: $ 7.5万
• 依托单位: Temple University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-05-15 至 2000-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9618521&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Actions; Finite; Groups

LORENZ ABSTRACT This award supports the research of Professor Martin Lorenz in the area of noncommutative ring theory with particular emphasis on the structure of rings of invariants arising from actions of finite groups and finite dimensional Hopf algebras. The main objectives will be the description of the Grothendieck groups G_0 and K_0 of these rings, the continued development of the representation theory of finite dimensional Hopf algebras, and the detailed analysis of invariant rings of multiplicative group actions on Laurent polynomial rings. Invariant theory and representation theory of groups are classical algebraic themes that are ubiquitous in pure mathematics and are indispensable in parts of applied mathematics and physics as well. Both are formally subsumed in the theory of Hopf algebras, more recent algebraic structures with a wide range of applications. In recognition of their relevance in physics, certain types of Hopf algebras are referred to as quantum groups. Hopf algebras further naturally arise in knot theory, an area of particular interest to molecular chemists as well as physicists.

洛伦兹摘要该奖项支持马丁·洛伦兹教授在非交通戒指理论领域的研究，特别着重于由有限群体和有限维度HOPF代数的行动引起的不变式戒指结构。 主要目标是对这些环的Grothendieck组G_0和K_0的描述，有限维数Hopf代数的表示理论的持续发展以及对Laurent多种元环的多liuldlical群体行为不变环的详细分析。 群体的不变理论和表示理论是经典的代数主题，在纯数学中无处不在，并且在应用数学和物理学的一部分中也是必不可少的。 两者正式归为HOPF代数理论，即最新的代数结构，具有广泛的应用。认识到它们在物理学上的相关性，某些类型的HOPF代数称为量子组。 HOPF代数进一步自然出现在结理论中，这是分子化学家和物理学家特别感兴趣的领域。