On a class of automorphisms in H2 which resemble the property of preserving volume

Jasna Prezelj and Fabio Vlacci

Mathematische Nachrichten, 2021, vol. 294, issue 4, 815-835

Abstract: We give a possible extension of definition of shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We define the divergence operator and determine the vector fields with divergence. Given the non‐existence of quaternionic volume form on H2, we define automorphisms with volume to be time‐one maps of vector fields with divergence and volume preserving automorphisms to be time‐one maps of vector fields with divergence 0. To these two classes the Andersen–Lempert theory applies. Finally, we exhibit an example of a quaternionic automorphism, which is not in the closure of the set of finite compositions of volume preserving quaternionic shears even though its restriction to the complex subspace C×C is in the closure of the set of finite compositions of complex shears.

Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201900259

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:294:y:2021:i:4:p:815-835

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().