Canonical coordinate systems and exponential maps of n-loop


Abstract


This paper is devoted to the study of canonical coordinate systems and the corresponding exponential maps of n-ary differentiable loops and to the discussion of their differentiability properties. Canonical coordinate systems can be determined by the canonical normal form of the power series expansion of the n-th power map x → x ○ x ○ ... ○ x ○ x.

DOI Code: 10.1285/i15900932v24n2p1

Keywords: Loops; n-ary systems; Local Lie groups

Classification: 20N05; 20N15; 22E05

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