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\(H\)-type groups and Iwasawa decompositions. (English) Zbl 0761.22010

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.

MSC:

22E25 Nilpotent and solvable Lie groups
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