Affine reductive spaces of small dimension and left \(A\)-loops

DOI10.1007/S00025-006-0216-2zbMATH Open1112.53040arXiv1506.08707OpenAlexW2963055599MaRDI QIDQ860129

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Publication date: 23 January 2007

Published in: (Search for Journal in Brave)

Abstract: In this paper we determine the at least $4$-dimensional affine reductive homogeneous manifolds for an at most $9$-dimensional simple Lie group or an at most $6$-dimensional semi-simple Lie group. Those reductive spaces among them which admit a sharply transitive differentiable section yield local almost differentiable left A-loops. Using this we classify all global almost differentiable left A-loops $L$ having either a $6$-dimensional semi-simple Lie group or the group $S{L}_3(mathbbR)$ as the group topologically generated by their left translations. Moreover, we determine all at most $5$-dimensional left A-loops $L$ with $PS{U}_3(mathbbC,1)$ as the group topologically generated by their left translations.

Full work available at URL: https://arxiv.org/abs/1506.08707

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