New York Journal of Mathematics
Volume 4 (1998) 177-183


Miloud Benayed and El Mamoun Souidi

Heisenberg Lie Bialgebras as Central Extensions

Published: October 8, 1998
Keywords: Heisenberg algebra, Lie bialgebras, central extensions
Subject: 16W30, 17B56

We determine and study all Lie bialgebra central extensions of R2n by R admitting the Heisenberg algebra H2n+1 as the underlying Lie algebra structure. The present work answers the question about the realizability of Lie bialgebra structures on H2n+1 as central extensions of R2n endowed with the adapted Lie bialgebra structure, by R.


The first author would like to thank G. Tuynman for discussions. The second author would like to thank G. Tuynman for the hospitality at Université de Lille I, and also C. Brezinski and J. Mikram, principal investigators of the grant Action Intégrée A/I 1036.

Author information

Miloud Benayed:
Université des Sciences et Technologies de Lille UFR de Mathématiques-URA au CNRS D751 59655 Villeneuve d'Ascq Cedex; France.

El Mamoun Souidi:
Université Mohammed V. Faculté des Sciences Département de Mathématiques et Informatique B.P 1014. Rabat; Maroc.