Moufang symmetry I. Generalized Lie and Maurer-Cartan equations

Abstract

The continuous Moufang loops are characterized as the algebraic systems where the associativity law is perturbed minimally. The minimal perturbation of associativity is characterized by the first- order partial differential equations, which in a natural way generalize the Lie and Maurer-Cartan equations from the theory of Lie groups.

arXiv comment6 pages, LaTeX2e, no figures. v2: exposition has been improved, the list of references remarkably extended

Cited by in corpus (8)

• Moufang symmetry IV. Reductivity and hidden associativity
• Moufang symmetry V. Triple closure
• Moufang symmetry III. Integrability of generalized Lie equations
• Moufang symmetry XI. Integrability of generalized Lie equations of continuous Moufang transformations
• Moufang symmetry VI. Reductivity and hidden associativity in Mal'tsev algebras
• Moufang symmetry X. Generalized Lie and Maurer-Cartan equations of continuous Moufang transformations
• Moufang symmetry XII. Reductivity and hidden associativity of infinitesimal Moufang transformations
• Linear representations of formal loops