Computational Cohomology for basic algebras
基本代数的计算上同调
基本信息
- 批准号:171121969
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:德国
- 项目类别:Priority Programmes
- 财政年份:2010
- 资助国家:德国
- 起止时间:2009-12-31 至 2014-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Experience shows that advances in the field of computational homological algebra lead to new theoretical insights, and that theoretical advances in turn result in better computational methods. By combining the work of several authors – including the applicant’s previous DFG project on the cohomology of p-groups – we will develop methods and software to compute cohomology rings and Ext-algebras for a variety of groups and basic algebras, using noncommutative Gröbner bases to construct minimal resolutions. This will allow us to compute a series of interesting test cases: both in group cohomology and for conjectures about finite dimensional algebras such as the Strong No Loops conjecture. The software will make use of the systems Gap and Singular, and will be made available as a Sage package. In addition to the design and implementation of suitable algorithms and the evaluation of the computational results obtained, we will also seek to generalise known degree bounds for cohomology rings to the case of Ext-algebras.
经验表明,计算同调代数领域的进步导致了新的理论见解,而理论的进步反过来又导致了更好的计算方法。通过结合几位作者的工作-包括申请人之前关于p群上同调的DFG项目-我们将开发方法和软件来计算各种群和基本代数的上同调环和ext -代数,使用非交换Gröbner基来构建最小分辨率。这将允许我们计算一系列有趣的测试用例:在群上同调和关于有限维代数的猜想,如强无环猜想。该软件将利用Gap和Singular系统,并将作为Sage软件包提供。除了设计和实现合适的算法以及评估所获得的计算结果外,我们还将寻求将上同环的已知度界推广到ext -代数的情况。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Professor Dr. David J. Green其他文献
Professor Dr. David J. Green的其他文献
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{{ truncateString('Professor Dr. David J. Green', 18)}}的其他基金
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