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International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 10, Pages 581-591

Normal Lie subsupergroups and non-abelian supercircles

Université Libre de Bruxelles, Campus Plaine, CP 218, bd du Triomphe, Brussels 1050, Belgium

Received 14 March 2001; Revised 3 September 2001

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose and study an appropriate analog of normal Lie subgroups in the supergeometrical context. We prove that the ringed space obtained taking the quotient of a Lie supergroup by a normal Lie subsupergroup, is still a Lie supergroup. We show how one can construct Lie supergroup structures over topologically nontrivial Lie groups and how the previous property of normal Lie subsupergroups can be used, in order to explicitly obtain the coproduct, counit, and antipode of these structures. We illustrate the general theory by carrying out the previous constructions over the circle, which leads to non-abelian super generalizations of the circle.