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What is a Mackey Obstruction?

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closed as not a real question by Loop Space, Dan Petersen, Daniel Moskovich, Leonid Positselski, Todd Trimble Apr 1 '11 at 18:33

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Hello, you are more likely to get an answer if you expand your question a little. What do you already know? What has led you to wanting to know about Mackey Obstructions? – Loop Space Apr 1 '11 at 12:17
Google is your friend, perhaps? – Yemon Choi Apr 1 '11 at 20:57

I think, it is the obstruction of extending a projective representation of a group to a linear one considered as an element of some H^2 cohomology group. This is quite standard and classical. You may find the definition in e.g. :

Curtis, Charles W.; Reiner, Irving Representation theory of finite groups and associative algebras. Reprint of the 1962 original. AMS Chelsea Publishing, Providence, RI, 2006.

Curtis, Charles W.; Reiner, Irving Methods of representation theory. Vol. I. With applications to finite groups and orders. Reprint of the 1981 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1990. xxiv+819 pp. ISBN: 0-471-52367-4, 20-02

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For a succinct answer, read a bit of Section 2 of this paper.

Also, there is a survey (the article by Judith Packer) of projective representations and the Mackey obstruction. "Projective representations and the Mackey obstruction - a survey", Contemporary Mathematics, v. 449 (2008), pp. 345-378.

(I posted this same reference as an answer to another question this morning, and am surprised that both of these questions weren't asked by the same person. You two should get together and talk...)

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