\(H\)-type groups and Iwasawa decompositions
type: Item
instance of: scholarly article
title: \(H\)-type groups and Iwasawa decompositions
zbMATH Open document ID: 0761.22010
DOI: 10.1016/0001-8708(91)90060-K
author: Anthony H. Dooley
author: Fulvio Ricci
author: Michael G. Cowling
author: Adam Korányi
published in: Advances in Mathematics
publication date: 1992-06-25T00:00:00Z
review text: The authors study a class of nilpotent Lie groups known as groups of Heisenberg type (or \(H\)-type groups). The subgroups \(N\) in the Iwasawa decompositions of real rank one simple Lie groups are of \(H\)-type. The authors give a simple Lie-algebraic condition which distinguishes such Iwasawa \(N\)-groups among all \(H\)-type groups. Then they discuss various problems in the geometry of \(H\)-type groups which are inspired by the known results about Iwasawa \(N\)-groups used in harmonic analysis.
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 10142
zbMATH Keywords: nilpotent Lie groups
zbMATH Keywords: groups of Heisenberg type
zbMATH Keywords: Iwasawa decompositions
Wikidata QID: Q56519595
reviewed by: Dragan Milicic
MaRDI profile type: Publication
cites work: Q3328752
cites work: Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one
cites work: Q3337675
cites work: The geometry of a semi-direct extension of a Heisenberg type nilpotent group
cites work: The contraction of K to \=NM
cites work: A fundamental solution for a subelliptic operator
cites work: Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups
cites work: Isospectral deformations of compact solvmanifolds
cites work: A duality for symmetric spaces with applications to group representations
cites work: Q3331943
cites work: Q4053537
cites work: Q5521308
cites work: Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
cites work: Riemannian nilmanifolds attached to Clifford modules
cites work: On the Geometry of Groups of Heisenberg Type
cites work: Q3671655
cites work: Intertwining operators for semisimple groups
cites work: Q3322322
cites work: Geometric properties of Heisenberg-type groups
cites work: Quasiconformal mappings on the Heisenberg group
cites work: On the existence and irreducibility of certain series of representations
cites work: Q3968106
cites work: Commutative Algebras of Invariant Functions on Groups of Heisenberg Type
cites work: The Automorphism Group of a Composition of Quadratic Forms
cites work: Explicit Spin Representations and Lie Algebras of Heisenberg Type
cites work: Q5522244
cites work: Intégrales d'entrelacement et fonctions de Whittaker
cites work: Geodesics and Conformal Transformations of Heisenberg-Reiter Spaces
cites work: Q4747189
full work available at URL: 0001-8708(91)90060-k
OpenAlex ID: W2045017310
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description: scientific article; zbMATH DE number 10142