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null Brüdern, Jörg / Bruinier, Jan Hendrik / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Gallavotti, Giovanni / Garnier, Josselin / Neeb, Karl-Hermann / Noguchi, Junjiro / Segal, Dan / Freydoon, Shahidi / Shigekawa, Ichiro / Sogge, Christopher D. / Strambach, Karl
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1Departamento de Matemática, Universidade de São Paulo, Caixa Postal 66281, São Paulo-SP, 05311-970, Brazil.
2Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary.
Citation Information: Forum Mathematicum. Volume 23, Issue 3, Pages 655–668, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/form.2011.032, April 2010
Publication History:
In this paper, we study the category of algebraic Bol loops over an algebraically closed field of definition. On the one hand, we apply techniques from the theory of algebraic groups in order to prove structural theorems for this category. On the other hand, we present some examples showing that these loops lack some nice properties of algebraic groups; for example, we construct local algebraic Bol loops which are not birationally equivalent to global algebraic loops.
Keywords.: Bol loops; algebraic loops; simple loops; algebraic groups as multiplication groups; local algebraic loops
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