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ASTRALGO Science 2016 Volume 2 1605

Moufang symmetry IV.
Reductivity and hidden associativity. Yamaguti brackets

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 Yamaguti brackets are introduced. It is shown how the integrability conditions of the generalized Lie equations of a local analytic Moufang loop lead to the reductivity conditions. By combining this result with the triality symmetry the Sagle-Yamaguti identity is proved.

5 pp, 8 Refs


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