Moufang symmetry I.
Associators and Akivis identity. Generalized Lie and MaurerCartan equations
E Paal
Tallinn University of Technology,
Estonia
Received 10 January 2008; Revised 17 December 2012, 21 March 2015
Abstract.
The continuous Moufang loops are characterized as the algebraic systems where the associativity law is minimally perturbed. The minimal perturbation of associativity is characterized by the firstorder partial differential equations, which in a natural way generalize the Lie and MaurerCartan equations of the Lie groups. The local associators are explicitly calculated and the Akivis identity is stated as well.
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