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Journal of Lie Theory 31 (2021), No. 4, 975--990
Copyright Heldermann Verlag 2021



On the Exponential Map of the Connected Isometry Group of a Damek-Ricci Space

Laura Geatti
Dip. di Matematica, UniversitÓ di Roma 2 Tor Vergata, Roma
geatti@mat.uniroma2.it

Martin Moskowitz
CUNY Graduate Center, New York, U.S.A.
martin.moskowitz@gmail.com



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.

Keywords: Damek-Ricci space, algebra of Heisenberg type, solvable group of exponential type, surjective exponential map, Clifford algebra.

MSC: 22E15, 22E25, 53C25, 53C30, 15A66.

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