Algebras with action and coaction of Hopf algebras

具有 Hopf 代数作用和相互作用的代数

• 批准号: 341792-2013
• 负责人: Kotchetov, Mikhail
• 金额: $ 0.8万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635411
• 关键词: Algebras; action; coaction; Hopf; algebras

My research area is the theory of Hopf agebras and its connections to noncommutative ring theory and Lietheory. Hopf algebras arise in many areas of mathematics and theoretical physics including knot and braidtheory, operator algebras, quantum theory and statistical mechanics. They provide a new unified approach tomany classical problems in algebra. There have been impressive recent advances in this field.The focus of the proposed research program will be on actions (or coactions) of Hopf algebras on otheralgebras. In particular, the theory of Hopf algebras gives a unified approach to the study of graded algebras,algebras with automorphisms, and algebras with derivations by viewing them as objects in an appropriatecategory associated to a Hopf algebra. Objects of this kind include so-called colour Lie superalgebras, whicharose in particle physics.The proposed research deals with classical objects of mathematics such as matrix algebras andfinite-dimensional simple Lie (super)algebras and is expected to contribute to the advancement of knowledgein fundamental areas of algebra. It may also find applications in other areas of mathematics and in theoreticalphysics.

我的研究领域是霍普夫代数理论及其与非交换环理论和李理论的联系。Hopf代数出现在数学和理论物理的许多领域，包括纽结和辫子理论，算子代数，量子理论和统计力学。它们为代数学中的任何经典问题提供了一种新的统一方法。最近在这一领域取得了令人印象深刻的进展，建议的研究计划的重点将是Hopf代数对其他代数的作用（或余作用）。特别是，Hopf代数的理论给出了一个统一的方法来研究分次代数，代数与自同构，代数与导子通过查看它们作为对象在一个适当的category相关联的一个Hopf代数。这类对象包括所谓的色李超代数，这在粒子物理学中很常见。拟议的研究涉及数学的经典对象，如矩阵代数和有限维简单李（超）代数，预计将有助于代数基础领域的知识进步。它也可以在数学和理论物理学的其他领域中找到应用。