Computational methods in nonassociative algebra

非结合代数的计算方法

• 批准号: 153128-2006
• 负责人: Bremner, Murray
• 金额: $ 0.8万
• 依托单位: University of Saskatchewan
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=339649
• 关键词: Computational; methods; nonassociative; algebra

The unifying theme of this research program is the developing connections between abstract algebra, computer science, and mathematical genetics. In abstract algebra, the focus is on using computational methods to study the classical theory of polynomial identities for nonassociative algebras.  Most of the classes of algebras studied by mathematicians are defined by identities (such as associative, Lie and Jordan algebras), and many of these structures have applications throughout mathematics and theoretical physics.  I am especially interested in the more recent applications to life sciences (in particular, DNA computing and population genetics) and in applications of biological theory to computer science (in particular, genetic algorithms). My research makes intensive use of computer algebra systems (such as Maple) to implement algorithms from linear algebra, combinatorics, and representation theory (of the symmetric group and of simple Lie algebras).

这个研究项目的统一主题是抽象代数、计算机科学和数学遗传学之间不断发展的联系。在抽象代数中，重点是用计算方法研究非结合代数的多项式恒等式的经典理论。数学家研究的大多数代数类都是由恒等式定义的（如结合代数、李代数和约当代数），其中许多结构在数学和理论物理中都有应用。我对最近在生命科学中的应用（特别是DNA计算和群体遗传学）和生物理论在计算机科学中的应用（特别是遗传算法）特别感兴趣。我的研究大量使用计算机代数系统（如Maple）来实现线性代数、组合学和表示理论（对称群和简单李代数）的算法。