Balogh and Tyson (Math Z 241(4):697–730, 2002) established the concept of polarizable Carnot groups, which are Carnot groups for which proper polar coordinates can be constructed. They also show that the groups of Heisenberg-type are polarizable and present an open question as to which Carnot groups are polarizable. Here, we explore the hidden nuance in this question as we demonstrate that polarization is not just a property of the algebraic group law, it is also dependent upon the Lie Algebra structure. We explore generalized Heisenberg-type groups and demonstrate the impact of the Lie Algebra.
Analysis and Mathematical Physics – Springer Journals
Published: Nov 10, 2020