Linear representations of formal loops
S. Madariaga, Jos\'e M. P\'erez-Izquierdo
TL;DR
This paper develops formulas for linear representations of formal loops, offering a new approach to their representation theory and revealing non-associative Moufang symmetry in groups.
Contribution
It introduces formulas for linear representations of formal loops and applies them to formal Moufang loops and Malcev algebras, uncovering non-associative Moufang symmetry.
Findings
Formulas for linear representations of formal loops
A new approach to Moufang loop and Malcev algebra representations
Identification of non-associative Moufang symmetry in groups
Abstract
A representation of an object in a category is an abelian group in the corresponding comma category. In this paper we derive the formulas describing linear representations of objects in the category of formal loops and apply them to obtain a new approach to the representation theory of formal Moufang loops and Malcev algebras based on Moufang elements. Certain 'non-associative Moufang symmetry' of groups is revealed.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · graph theory and CDMA systems