International Journal of Mathematics and Mathematical Sciences
Volume 2008 (2008), Article ID 632518, 9 pages
doi:10.1155/2008/632518
Research Article

Lie Supergroups Obtained from 3-Dimensional Lie Superalgebras Associated to the Adjoint Representation and Having a 2-Dimensional Derived Ideal

I. Hernández1 and R. Peniche2

1CIMAT, Apdo. Postal 402, C.P., Guanajuato 36000, GTO, Mexico
2Facultad de Matemáticas, Universidad Autónoma de Yucatán, Apdo. Postal 172, C.P., Mérida 97110, YUC, Mexico

Received 18 January 2007; Revised 23 May 2007; Accepted 31 October 2007

Academic Editor: Nils-Peter Skoruppa

Copyright © 2008 I. Hernández and R. Peniche. 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.

Abstract

We give the explicit multiplication law of the Lie supergroups for which the base manifold is a 3-dimensional Lie group and whose underlying Lie superalgebra g=g0⊕g1which satisfies g1=g0, g0 acts on g1 via the adjoint representation and g0 has a 2-dimensional derived ideal.