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ASTRALGO Science 2016 Volume 2 1602

Moufang symmetry I.
Associators and Akivis identity. Generalized Lie and Maurer-Cartan equations

E Paal
Tallinn University of Technology, Ehitajate tee 5, 19086 Tallinn, 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 first-order partial differential equations, which in a natural way generalize the Lie and Maurer-Cartan equations of the Lie groups. The local associators are explicitly calculated and the Akivis identity is stated as well.

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