Workshop for new faculty and graduate students on Lattice-Ordered Groups and MV-Algebras

为新教师和研究生举办的关于格序群和 MV 代数的研讨会

• 批准号: 0901560
• 负责人: Warren McGovern
• 金额: $ 2.04万
• 依托单位: Bowling Green State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0901560&HistoricalAwards=false
• 关键词: Workshop; new; faculty; graduate; students

Principal Investigator: McGovern, Warren Wm.Proposal Number: 0901560Institution: Bowling Green State UniversityTitle: Workshop for new faculty and graduate students on Lattice-Ordered Groups and MV-AlgebrasAbstract: The Department of Mathematics and Statistics at Bowling Green State University (Ohio, USA) will host a workshop on lattice-ordered groups and MV-algebras June 8th through June 12th. The workshop will provide a very important opportunity to new researchers (including graduate students) to work with experts from the two fields. The workshop will be followed by the 12th annual International Conference on Ordered Algebraic Structures which will run from the 15th of June through the 19th of June. The theory of lattice-ordered groups has a long history and has many applications to other branches of mathematics: lattice theory, permutation groups, commutative integral domains, vector lattices, positivity, algebraic K-theory, and general topology. MV-algebras (or ?many-valued algebras?) were introduced in the 1950s by C.C. Chang to form the algebraic semantics of Lukasiewicz many-valued logic. The theory of MV-algebras has applications to logic, toric varieties, algebraic K-theory, functional analysis, and C*-algebras. In 1986, D. Mundici proved that the category of abelian lattice-ordered groups with strong order unit and their unit-preserving homomorphisms is naturally equivalent to the category of MV-algebras. In 2002 this result was extended to a natural equivalence between the category of lattice-ordered groups with strong order unit and their unit-preserving homomorphisms and the category of generalized MV-algebras (a.k.a. pseudo MV-algebras).The workshop aims to inform its participants on the recent breakthroughs of how the two branches of mathematics interact with each other. It is hoped that the workshop will lead to further developments and connections between the two fields. One of the main goals of the workshop is to expose new faculty and graduate students, including members of under represented groups, to the two branches of mathematics and have them interact with experts in the fields. The participants will also be afforded the opportunity to participate in the 12th annual International Conference on Ordered Algebraic Structures which immediately follows the workshop. For more information about the workshop, please see the following webpage:http://www-math.bgsu.edu/~warrenb/Workshop/Workshop09.html

首席研究员：McGovern， Warren Wm。摘要：美国俄亥俄州鲍灵格林州立大学数学与统计系将于6月8日至6月12日举办一场关于格序群和v -代数的研讨会。研讨会将为新的研究人员（包括研究生）提供一个与这两个领域的专家合作的非常重要的机会。研讨会之后是第12届有序代数结构年度国际会议，会议将于6月15日至6月19日举行。格序群的理论有着悠久的历史，在数学的其他分支中有许多应用：格理论、置换群、交换积分域、向量格、正性、代数k理论和一般拓扑。mv -代数(或？（多值代数？）是在20世纪50年代由C.C. Chang引入的，用以形成Lukasiewicz多值逻辑的代数语义。mv -代数理论在逻辑、环变、代数k -理论、泛函分析和C*-代数中都有应用。1986年，D. Mundici证明了具有强序单位的阿贝尔格序群及其保单位同态的范畴与v -代数的范畴自然等价。2002年将这一结果推广到具有强序单位的格序群及其保单位同态的范畴与广义mv -代数（又称伪mv -代数）的范畴之间的自然等价。研讨会的目的是向参与者介绍数学的两个分支如何相互作用的最新突破。希望讲习班将导致这两个领域之间的进一步发展和联系。研讨会的主要目标之一是让新的教师和研究生，包括代表性不足的群体的成员，接触数学的两个分支，并让他们与该领域的专家互动。与会者还将有机会参加紧随讲习班之后的第12届有序代数结构国际年度会议。有关研讨会的详情，请浏览以下网页：http://www-math.bgsu.edu/~warrenb/Workshop/Workshop09.html