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Publicly Available Published by De Gruyter November 18, 2008

The multiplication groups of 2-dimensional topological loops

  • Ágota Figula
From the journal Journal of Group Theory

Abstract

If the multiplication group Mult(L) of a connected simply connected 2-dimensional topological loop L is a Lie group, then Mult(L) is an elementary filiform Lie group ℱ of dimension n + 2 for some n ⩾ 2, and any such group is the multiplication group of a connected simply connected 2-dimensional topological loop L. Moreover, if the group topologically generated by the left translations of L has dimension 3, then L is uniquely determined by a real polynomial of degree n.

Received: 2008-04-08
Revised: 2008-07-28
Published Online: 2008-11-18
Published in Print: 2009-May

© de Gruyter 2009

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