New York Journal of Mathematics
Volume 21 (2015) 1247-1261


Béchir Dali

Note on the cortex of some exponential Lie groups

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Published: November 22, 2015
Keywords: Nilpotent and solvable Lie groups, orbit method, unitary representations of locally compact Lie groups.
Subject: 22E25, 22E15, 22D10

In this paper, we built a family of 4d-dimensional two-step nilpotent Lie algebras (\frak gd)d≧ 2 so that the cortex of the dual of each \frak gd is a projective algebraic set. We also give a complete description of the cortex of the exponential connected and simply connected Lie group G=Rn\rtimesR.


The author would like to extend his sincere appreciation to the Deanship of Scientific Research at king Saud University for its funding through Research group RG-1435-069.

Author information

Department of Mathematics, Faculty of sciences of Bizerte, 7021 Zarzouna, Bizerte, Tunisia
Current Address: King Saud University, College of Science, Department of Mathematics, Riyadh, P.O Box 2455, Riyadh 11451, K.S.A.