TRIPLE TORTKEN IDENTITIES

N. A. Mardanov
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Abstract

We define a triple Tortken product in Novikov algebras. Using computer algebra calculations, we give a list of polynomial identities up to degree 5 satisfied by Tortken triple product in every Novikov algebra. It has applications in theoretical physics, specifically in the field of quantum field theory and topological field theory. A Novikov algebra is defined as a vector space equipped with a binary operation called the Novikov bracket. The Jacobi identity ensures that the Novikov bracket behaves analogously to the commutator in Lie algebras. However, unlike Lie algebras, Novikov algebras are non-associative due to the presence of the Jacobi identity rather than the associativity condition. Novikov algebras find applications in theoretical physics, particularly in the study of topological field theories and quantum field theories on noncommutative spaces. They provide a framework for describing and analyzing certain algebraic structures that arise in these areas of physics. It's worth noting that Novikov algebras are a specific type of non-associative algebra, and there are various other types of non-associative algebras studied in mathematics and physics, each with its own defining properties and applications.
三重扭曲身份
我们在Novikov代数中定义了三重Tortken积。利用计算机代数计算,给出了每一个诺维科夫代数中Tortken三重积满足的5次多项式恒等式的一个列表。它在理论物理中有应用,特别是在量子场论和拓扑场论领域。一个诺维科夫代数被定义为一个具有称为诺维科夫括号的二进制运算的向量空间。雅可比恒等式保证了诺维科夫括号的行为类似于李代数中的对易子。然而,与李代数不同的是,Novikov代数是非结合性的,这是由于Jacobi恒等式而不是结合性条件的存在。诺维科夫代数在理论物理中有广泛的应用,特别是在非交换空间的拓扑场论和量子场论的研究中。它们为描述和分析这些物理领域中出现的某些代数结构提供了一个框架。值得注意的是,诺维科夫代数是一种特殊类型的非结合代数,在数学和物理中还研究了各种其他类型的非结合代数,每种代数都有自己的定义性质和应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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