TRIPLE TORTKEN IDENTITIES

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.