Linear representations of formal loops
arXiv:1503.07013
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.
31 pages
References in corpus (10)
- Moufang symmetry IV. Reductivity and hidden associativity
- Moufang symmetry VII. Moufang transformations
- Moufang symmetry VIII. Reconstruction of Moufang loops
- Moufang symmetry V. Triple closure
- Moufang symmetry III. Integrability of generalized Lie equations
- Moufang symmetry II. Moufang-Mal'tsev pairs and triality
- Moufang symmetry VI. Reductivity and hidden associativity in Mal'tsev algebras
- Moufang symmetry XI. Integrability of generalized Lie equations of continuous Moufang transformations
- Moufang symmetry XII. Reductivity and hidden associativity of infinitesimal Moufang transformations
- Moufang symmetry X. Generalized Lie and Maurer-Cartan equations of continuous Moufang transformations