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

主要研究人员：麦戈文，Warren Wm.建议编号：0901560机构：保龄格林州立大学标题：格序群和MV-代数新教师和研究生研讨会摘要：鲍林格林州立大学(美国俄亥俄州)数学和统计系将于6月8日至6月12日举办关于格序群和MV-代数的研讨会。研讨会将为新的研究人员(包括研究生)提供一个非常重要的机会，让他们与这两个领域的专家合作。研讨会之后将举行第12届国际有序代数结构会议，会议将于6月15日至19日举行。格序群理论有很长的历史，并在其他数学分支中有许多应用：格论、置换群、交换整环、向量格、正性、代数K-理论和一般拓扑学。MV-代数(或多值代数？)等人在20世纪50年代引入了Lukasiewicz多值逻辑的代数语义。MV-代数理论在逻辑、环簇、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交换格序群及其保单位同态范畴与MV-代数范畴自然等价。2002年，这一结果被推广到具有强序单位及其保单位同态的格序群范畴与广义MV-代数范畴(又名)之间的自然等价。伪MV-代数)。研讨会的目的是向学员介绍这两个数学分支如何相互作用的最新突破。希望该讲习班将导致这两个领域之间的进一步发展和联系。讲习班的主要目标之一是让新的教职员工和研究生，包括代表性不足群体的成员，接触数学的两个分支，并让他们与该领域的专家进行互动。与会者还将有机会参加在讲习班之后立即举行的第十二届国际有序代数结构会议。有关研讨会的更多信息，请访问以下webpage:http://www-math.bgsu.edu/~warrenb/Workshop/Workshop09.html

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