We prove that the connected isometry group of a non symmetric (non compact) irreducible Damek-Ricci space has a surjective exponential map if and only if the center of the associated Heisenberg type algebra has dimension less than or equal to 5. This result is analogous to (and extends) the results proved by the second author concerning the exponential map of the connected isometry group of an irreducible, rank one, classical, symmetric space of non compact type and that of D. Djokovic and N. Thang [On the exponential group of almost simple real algebraic groups, J. Lie Theory 5 (1996) 275--291] in the case of the Cayley plane to all irreducible non compact DR spaces.
Classification :
22E15, 22E25, 53C25, 53C30, 15A66
Mots-clés :
Damek-Ricci space, algebra of Heisenberg type, solvable group of exponential type, surjective exponential map, Clifford algebra
Affiliations des auteurs :
Laura Geatti
1
;
Martin Moskowitz
2
1
Dip. di Matematica, Università di Roma 2 Tor Vergata, Roma
2
CUNY Graduate Center, New York, U.S.A.
Laura Geatti; Martin Moskowitz. On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space. Journal of Lie Theory, Tome 31 (2021) no. 4, pp. 975-990. http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a4/
@article{JOLT_2021_31_4_a4,
author = {Laura Geatti and Martin Moskowitz},
title = {On the {Exponential} {Map} of the {Connected} {Isometry} {Group} of a {Damek-Ricci} {Space}},
journal = {Journal of Lie Theory},
pages = {975--990},
year = {2021},
volume = {31},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a4/}
}
TY - JOUR
AU - Laura Geatti
AU - Martin Moskowitz
TI - On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space
JO - Journal of Lie Theory
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SP - 975
EP - 990
VL - 31
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a4/
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%V 31
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%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_4_a4/
%F JOLT_2021_31_4_a4
