Conference on Nonassociative Algebra in Action: Past, Present, and Future Perspectives

行动中的非结合代数会议：过去、现在和未来的观点

• 批准号: 1106203
• 负责人: Weiqiang Wang
• 金额: $ 1.3万
• 依托单位: University of Virginia Main Campus
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-05-01 至 2012-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106203&HistoricalAwards=false
• 关键词: Conference; Nonassociative; Algebra; Action; Past

This conference brings together researchers who have contributed to diverse and unanticipated applications of nonassociative algebras and nonassociative methods in mathematics, including Zelmanov's solution of the restricted Burnside problem using quadratic Jordan algebras , the use of Poisson brackets by Shestakov and Umirbaev in settling Nagata's conjecture on polynomial algebra symmetries, and Griess's construction of the Monster finite simple group through automorphisms of a new nonassociative algebra. Other areas of impact represented at the conference include include extended affine Lie algebras, and the arithmetic study of algebraic groups, and somewhat more classical applications include finite and continuous geometry, such as projective planes and bounded symmetric domains.To most mathematicians or physicists, Lie algebras are the most familiar examples of nonassociative algebra, known for over a hundred years as an efficient way of algebraically dealing with rules of constraint imposed by interactions in physics. Later, another type of nonassociative algebras, called Jordan algebras, was proposed as part of a possible alternative foundation for quantum physics . Soon, it was realized there were many different types of nonassociative algebras that might be worth studying, and in the 60s and 70s there was a serious study of these algebras for their own sake, an effort including mathematicians from Yale, Chicago, MIT, as well as the former Soviet Union. Though this original activity impacted mainly Lie algebras and bounded symmetric domains, the subject slowly began to have surprising new applications. This new activity took place over a period of about thirty years, beginning in the 80s, in areas not obviously related to the problems which had given it birth. While there have been, of course, conferences in the many separate areas where nonassociative algebras have been used, there have been none attempting to draw together so many of these disparate applications, and compare them for the benefit of new generations of mathematicians. It is the purpose of this conference to help these new generations and all present better understand the ways in which nonassociative algebras might be used even more broadly, to foster possible new collaborations, and to help discover the most productive directions for future research.

This conference brings together researchers who have contributed to diverse and unanticipated applications of nonassociative algebras and nonassociative methods in mathematics, including Zelmanov's solution of the restricted Burnside problem using quadratic Jordan algebras , the use of Poisson brackets by Shestakov and Umirbaev in settling Nagata's conjecture on polynomial algebra symmetries, and Griess通过新的非社交代数的自动形态构建了怪物有限的简单群体。会议上代表的其他影响领域包括扩展的仿射谎言代数，以及对代数群体的算术研究，而更古典的应用包括有限的几何形状，例如投射平面和有界的对称域。对于大多数数学家或物理学家而言，对于多种熟悉的代数典型的典范，是一种非疗法的范围，这是一个熟悉的效果。代数处理物理相互作用施加的约束规则。后来，提出了另一种称为约旦代数的非缔合代数，作为量子物理学的替代基础的一部分。很快，人们意识到可能值得研究的是许多不同类型的非社交代数，而在60年代和70年代，为了自己的缘故，对这些代数进行了认真的研究，其中包括来自耶鲁，芝加哥，麻省理工学院，麻省理工学院以及前苏联联盟的数学家。尽管这种原始活动主要影响代数和有限的对称域，但该受试者逐渐开始具有令人惊讶的新应用。这项新活动发生在大约三十年的时间里，从80年代开始，在与出生的问题不显着有关的领域。当然，尽管已经使用了非缔约代数的许多独立领域中的会议，但没有试图将许多不同的应用程序汇集在一起​​，并将其比较，并为新一代数学家的利益进行比较。这是本次会议的目的，以帮助这些新一代，并且所有人都更好地了解了可以更广泛地使用非社交代数的方式，以促进可能的新合作，并帮助发现未来研究的最有效的方向。