Groebner bases for algebraic systems and homology, homotopy

代数系统和同源、同伦的 Groebner 基

基本信息

批准号：
14540046
负责人：
KOBAYASHI Yuji
金额：
$ 1.15万
依托单位：
Toho University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

项目摘要

Recently, various decision problems on algebraic systems defined by a finite number of generators and relations (finitely presented algebraic systems) have been studied extensively because of relationship to computation theory.In this research, we studied finitely presented algebraic systems, in particular, finitely presented monoids and associative algebras in terms of rewriting systems. We investigated conditions for algebraic systems to have finite complete rewriting systems and relationship to homology and homotopy.If a monoid has a finite complete rewriting system, then it satisfies the homological finiteness property FP3 and the homotopical finiteness property FDT (by Squier). Pride introduced another homological finiteness property FHT and showed that FHT follows from FDT. We showed that FHT is equivalent to bi-FP3 for finite presented monoids in the third paper in REFERENCES.It is well-known that many properties on finitely presented monoids are (recursively) undecidable. We pr … More oved in the first paper that they are undecidable even for finitely presented monoids with word problem decidable in linear time. Moreover, in the second paper we showed that many homological properties of monoids are also undecidable. Results about the undecidability of the centers of groups and group algebras will be published in a forthcoming paper (the sixth paper).In the fifth paper we developed the theory of Groebner bases on general associative algebras and their free bimodules from a viewpoint of rewriting systems and applied it to compute the Hochschild cohomology of algebras. This is the main results of this research, and we expect to apply them to more general (or special) algebraic systems.In the forth paper we gave a method to study Enriques surfaces via Enriques lattices.In February, 2002 at Kyoto Research Institute of Mathematical Science, in December at Kanagawa Institute of Technology, and in December, 2003 at Toho University we hold research meetings on algebraic systems and computations. The results are compiled into a research report in the seventh article in REFERENCES Less

最近，由于与计算理论的关系，我们已经进行了广泛的研究。在这项研究中，我们在此研究中呈现了有限介绍的系统，尤其是在重新调查的系统中，我们研究了有限的系统。同源性和同质性。如果单型具有有限的完整重写系统，则满足同源性属性属性FP3和同源有限属性属性FDT（由Squier）。 Pride引入了另一个同源性属性FHT，并表明FHT来自FDT。我们表明，在参考文献中第三篇论文中，FHT等于BI-FP3。我们……在第一篇论文中，更多的烤箱即使最终呈现了单词问题，它们在线性时间中决定了。此外，在第二篇论文中，我们表明许多单体的同源特性也是无法执行的。关于团体和组代数中心的不可申请的结果将在即将发表的论文（第六篇论文）中发表。在第五篇论文中，我们从重写系统的观点中开发了关于一般协会代数及其免费的Bimodules的Groebner基础理论，并将其应用于Alge alge alge of Algebras。这是这项研究的主要结果，我们希望将它们应用于更通用（或特殊的）代数系统。在第四篇论文中，我们提供了一种通过Enriques lattices来研究Enriques表面的方法。2002年2月在京都数学研究所在12月在Kanagawa Science在Kanagawa技术研究所以及2003年12月在2003年12月在Toho System Inturn Insuptions and toho Insuction and The Incultion Insuctions和Insuctions Insuctions and toho Insuction。结果在第七篇文章中汇编为参考文献少的研究报告