کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6425821 | 1633843 | 2013 | 24 صفحه PDF | دانلود رایگان |
The famous Baker-Campbell-Hausdorff series defines a group composition on the set of the so called grouplike elements of a completed free Lie algebra as we can find in P. Cartier's paper on the Campbell-Hausdorff formula in 1956. According to A. Baider and R.C. Churchill, we call this group the Campbell-Hausdorff group over the alphabet X of the free Lie algebra. By a certain coproduct and certain bialgebra endomorphisms of the free associative algebra over a set X which should be at most countably infinite, we get an alternative realisation of this Campbell-Hausdorff group. This realisation is much more comfortable to deal with than the classical one. The usual composition of endomorphisms gives a near-ring structure to this group. In this paper we consider a metric on the Campbell-Hausdorff near-ring over the alphabet N and the compatibility of this metric with the near-ring compositions and we make some topological remarks.
Journal: Advances in Mathematics - Volume 245, 1 October 2013, Pages 113-136