Linear representations of formal loops

2015/03/24 by Sara Madariaga, Madariaga, S., José M. Pérez-Izquierdo +1
Engineering · Mathematics · #17D10 #20N05 #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1503.07013

openalex publication_date 2015/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Moufang symmetry V. Triple closure
• Moufang symmetry XI. Integrability of generalized Lie equations of continuous Moufang transformations
• Moufang symmetry II. Moufang-Mal'tsev pairs and triality

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