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arXiv · 1810.11412

On a class of automorphisms in $\mathbb{H}^2$ which resemble the property of preserving volume

Jasna Prezelj·Fabio Vlacci
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Abstract

We give a possible extension for shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We present a possible definition of volume preserving automorphisms, even though there is no quaternionic volume form on $\mathbb{H}^2$ . Using this, we determine a class of quaternionic automorphisms for which the Ander- sen-Lempert theory applies. Finally, we exhibit an example of a quaternionic automor- phism, which is not in the in the closure of the set of finite compositions of volume preserving quaternionic shears.

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Jasna Prezelj, Fabio Vlacci. 2018-10-26. On a class of automorphisms in $\mathbb{H}^2$ which resemble the property of preserving volume. https://arxiv.org/abs/1810.11412

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