TL;DR
This paper investigates the algebraic structure of bilinear multiplications on n-dimensional vector spaces, focusing on the Kantor product applied to various well-known algebraic systems such as associative, Lie, and Novikov algebras.
Contribution
It introduces a detailed study of the Kantor product in the context of different algebraic structures, expanding understanding of their interactions and properties.
Findings
Kantor product applied to associative algebras
Kantor product in Lie algebras
Analysis of Kantor product in Novikov and alternative algebras
Abstract
We study the algebra of bilinear multiplications of an -dimensional vector space. In particular, we study the Kantor product of some well-known (associative, Lie, alternative, Novikov and some other) multiplications.
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