Geometric analysis on <i>H</i> ‐type groups related to division algebras

Abstract

Abstract The present article applies the method of Geometric Analysis to the study H ‐type groups satisfying the J 2 condition and finishes the series of works describing the Heisenberg group and the quaternion H ‐type group. The latter class of H ‐type groups satisfying the J 2 condition is related to the octonions. The relations between the group structure and the boundary of the corresponding Siegel upper half space are given. (© 2009 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)