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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:
 2.2e+26 Nilpotent and solvable Lie groups
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##### References:
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