From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4422 Path: news.gmane.org!not-for-mail From: Johannes Huebschmann Newsgroups: gmane.science.mathematics.categories Subject: injective modules over a Lie groupoid Date: Tue, 10 Jun 2008 22:20:13 +0200 (CEST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019937 13221 80.91.229.2 (29 Apr 2009 15:45:37 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:37 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Jun 10 19:27:00 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 10 Jun 2008 19:27:00 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1K6C6o-00053T-3Y for categories-list@mta.ca; Tue, 10 Jun 2008 19:14:30 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 3 Original-Lines: 56 Xref: news.gmane.org gmane.science.mathematics.categories:4422 Archived-At: Dear All For a Lie group G and a vector space V, C^{\infty}(G,V) is a differentiably injective G-module (Hochschild-Mostow). Is there an analoguous construction for a Lie groupoid or, in the algebraic setting, cogroupoid object in the category of commutative algebras? Let G be a Lie groupoid, with object manifold G_o, source and target maps being supposed surjective submersions. A G-module is a vector bundle V \to G_o on G_o with a G-structure (pairing G x_G_o V to V over G_o satisfying the obvious compatiblity conditions). If we start with a vector bundle V to G_o on G_o, what corresponds to the construction C^{\infty}(G,V) for the special case where G is an ordinary Lie group? More generally, G being a Lie groupoid, does the category of G-modules have enough injectives? Where in the literature can I find answers to these questions if any? Many thanks in advance Regards Johannes HUEBSCHMANN Johannes Professeur de Mathematiques USTL, UFR de Mathematiques UMR 8524 Laboratoire Paul Painleve F-59 655 Villeneuve d'Ascq Cedex France http://math.univ-lille1.fr/~huebschm TEL. (33) 3 20 43 41 97 (33) 3 20 43 42 33 (secretariat) (33) 3 20 43 48 50 (secretariat) Fax (33) 3 20 43 43 02 e-mail Johannes.Huebschmann@math.univ-lille1.fr