Journal of Lie Theory

no. 4
On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space
Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 975-990
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.
DOI: 10.5802/jolt.1204
Classification: 22E15, 22E25, 53C25, 53C30, 15A66
Keywords: Damek-Ricci space, algebra of Heisenberg type, solvable group of exponential type, surjective exponential map, Clifford algebra 
@article{JOLT_2021_31_4_a4,
     author = {L. Geatti and M. 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},
     doi = {10.5802/jolt.1204},
     zbl = {1489.22003},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1204/}
}
TY  - JOUR
AU  - L. Geatti
AU  - M. Moskowitz
TI  - On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space
JO  - Journal of Lie Theory
PY  - 2021
SP  - 975
EP  - 990
VL  - 31
IS  - 4
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1204/
DO  - 10.5802/jolt.1204
ID  - JOLT_2021_31_4_a4
ER  - 
%0 Journal Article
%A L. Geatti
%A M. Moskowitz
%T On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space
%J Journal of Lie Theory
%D 2021
%P 975-990
%V 31
%N 4
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1204/
%R 10.5802/jolt.1204
%F JOLT_2021_31_4_a4
L. Geatti; M. Moskowitz. On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space. Journal of Lie Theory, Volume 31 (2021) no. 4, pp. 975-990. doi: 10.5802/jolt.1204

Cited by Sources: