Talk:Lie algebroid

Reference to the correct type of stack

There was a wikilink in the Examples section from the word stacky to Stack (category theory), which has now been split. Based on the context, I've redirected towards Algebraic stack, which continues to have the subject matter of the old article. It seems, however, that rather than an algebraic stack the actually proper reference should be to the differential-geometric analogue of an algebraic (presumably Deligne-Mumford type) stack. However, these objects do not yet have a page. A quick reference to such objects will be added to algebraic stacks, together with a brief explanation of how they relate to various types of étendues (the topos-theoretic analogue). If the above is a misunderstanding of the context on this page and that the link should point elsewhere, please do fix it. Stca74 09:07, 10 September 2007 (UTC)

added section about associated Lie algebroid

It is certainly a quite short explanation, but is it also comprehensible for someone dealing with differential geometry? I have added an explicit example to clarify the relation between the target map and left-invariant vector fields/ functions. Should I be more explicit about this correlation?

Of course there are some proofs neglected behind the statements of identification, ... . These follow from elementary properties in differential geometry and are left to the reader.

[melli]64.178.100.37 (talk) 09:11, 24 February 2008 (UTC)

still stub?

Could someone mention further topics you wish to be added before the article is no longer considered stub? [melli] 64.178.100.37 (talk) 09:19, 24 February 2008 (UTC)

Probably, exterior differentiation and Schouten Gerstenhaber algebra associated to a Lie algebroids (actually, equivalent presentations) are needed, in my opinion (193.137.102.7 (talk) 17:38, 25 November 2008 (UTC)).

Not a stub any longer. 67.198.37.16 (talk) 21:16, 29 May 2024 (UTC)

Missed Def of the anchor map

The definition of the anchor map in the construction of the Lie algebroid of a Lie groupoid is missing.

Definition of morphism must be included, too. — Preceding unsigned comment added by 92.226.55.226 (talk) 10:43, 11 November 2011 (UTC)

This all seems to be in place, now. 67.198.37.16 (talk) 21:26, 29 May 2024 (UTC)

Help with example

Does anyone know how to figure out the anchor map for the example I wrote up? — Preceding unsigned comment added by Username6330 (talk • contribs) 22:27, 10 November 2017 (UTC)

Unspecified symbol

I think one should define the dot product in the first equation.217.234.135.12 (talk) 14:18, 3 October 2018 (UTC)

Excellent question. From context, it is some bundle metric. It's deeply disconcerting that this is not spelled out explicitly, since, it seems to me that there's a lot of room for fiddle-faddle just right there. I left a message for User:Francesco Cattafi, who is the reigning expert on this topic, based on edit history. 67.198.37.16 (talk) 20:50, 29 May 2024 (UTC)

Oh, effing a. $\rho (X)f$ is just a friggin scalar, so this is just a simple scalar product. Dohhh! Updating article now. 67.198.37.16 (talk) 21:19, 29 May 2024 (UTC)

Notation for vector bundle

In relation to he question above, this article currently writes that $A\to M$ is a vector bundle, rather than the more conventional $\pi :A\to M$. This is a really minor point, but would help with clarity overall. I'm not making this change, if only because I don't know what notation the Lie algebroid community prefers for this. 67.198.37.16 (talk) 21:14, 29 May 2024 (UTC)