Talk:Poisson manifold

Problem

I think there is a problem with the condition on this page. It says "provided that ...", which is followed by a sum, but no equal sign (equivalence operator). I guess that as a condition this sum of permutations should be equal to something, possibly 0.

Is this copied from a book?

I noticed that this whole page is eerily similar to section 1.1 of Chari & Pressley, /A guide to quantum groups/. In fact, it reads like it was typewritten directly from the book. Looking at the history, I can't tell whether this is just coincidence, but shouldn't we at least cite Chari & Pressley? TorstenSchoenfeld (talk) 13:11, 16 December 2009 (UTC)

I wrote this long, long ago with a copy of Chari & Pressley in my lap; the goal was to avoid stupid mistakes, rather than to transcribe. (writing from memory is an excellent way of making stupid mistakes). Perhaps I got carried away. Why I did not stick it in as a reference, I dunno. 67.198.37.16 (talk) 22:36, 10 November 2020 (UTC)

complex Poisson terminology

Note that one needs to be very careful using the term "complex Poisson" this way: this is what Chari and Pressley do, but one should be aware that the notion of complex symplectic manifold (=holomorphic symplectic manifold) is not a complex Poisson manifold in this sense (it has a holomorphic Poisson bivector, i.e. a section of wedge^2 of the holmorphic tangent bundle). For example if G=GL_n(C), then the dual of the Lie algebra of G is a holmorphic Poisson manifold, and its symplectic leaves are complex symplectic manifolds.

Since the terms complex symplectic=holomorphic symplectic are entrenched I would suggest to define a complex Poisson manifold to be a holomorphic Poisson manifold and to find another term for the objects discussed here (and in Chari-Pressley). — Preceding unsigned comment added by 78.239.179.184 (talk) 10:02, 1 March 2012 (UTC)

Ichthyomorphism

Under the "Poisson maps" section, the term 'ichthyomorphism' is introduced. Is this term standard in the literature? I've tried to find an origin of the term, but this Wikipedia page appears to be the only source of it. I've not been able to find any older use of it. Was the term invented on this page? Could someone clarify this?

If you use Google Scholar to search for 'ichthyomorphism', you will find a few references to it in biology and various bio-related fields. A more common word is 'ichthyomorphic', which can even be found in the Mirriam-Webster dictionary and others. I do not know why it appears here. Sounds fishy. MidwestGeek (talk) 05:14, 3 May 2019 (UTC)