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On the Lie Algebra of polarizable Carnot groups

On the Lie Algebra of polarizable Carnot groups 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

On the Lie Algebra of polarizable Carnot groups

Analysis and Mathematical Physics , Volume 10 (4) – Nov 10, 2020

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Publisher
Springer Journals
Copyright
Copyright © Springer Nature Switzerland AG 2020
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-020-00438-4
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Nov 10, 2020

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