added pointer to:

- Ernst Binz, Sonja Pods,
*The geometry of Heisenberg groups β With Applications in Signal Theory, Optics, Quantization, and Field Quantization*, Mathematical Surveys and Monographs**151**, American Mathematical Society (2008) [ams:surv-151]

(here and elsewhere, such as at *Heisenberg Lie algebra*)

I have been expanding and polishing the entry *Heisenberg group*.

This had existed in bad shape for quite a while, but now itβs maybe getting into better shape.

I tried to spend some sentences on issues which I find are rarely highlighted appropriately in the literature. So there is discussion now of the fact that

there are different Lie groups for a given Heisenberg Lie algebra,

and the appearance of an β$i$β in $[q,p] = i$ may be all understood as not picking the simply conncted ones of these;

I also added remarks on the relation to Poisson brackets, and symplectomorphisms.

In this context: either I am dreaming, or there is a mistake in the Wikipedia entry *Poisson bracket - Lie algebra*.

There it says that the Poisson bracket is the Lie algebra of the group of symplectomorphisms. But instead, it is the Lie algebra of a central extension of the group of Hamiltonian symplectomorphisms.

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