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I am looking for an as gentle and pedagogical as possible introduction that explains the Virasoro algebra and its applications in theoretical physics; finally I am interested in its application in string theory.

The short explanations in the physics books I am reading are not enough to make me feel comfortable about the Virasoro algebra so I need to read some more ...

I prefer shorter than whole book references which are optimally freely accessible, but if this does not work other things are welcome too.

I know a little bit about Lie algebras and conformal transformations, but the central extension issue confuses me. What I am looking for could be something at the level of these BRST lecture notes I could mostly follow.

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The V. Algebra is a central extension of a Lie algebra of conformal complex transformations. As simple as you'd like it it is going to require full, or close to full undergraduate algebra (or even beyond), complex analysis and odds are it is not going to be very gentle, and much even less if you want the applications to String Theory. Perhaps the best to do with this is to approach someone who masters the subject and learn directly from him. – DonAntonio Apr 3 '13 at 17:10
@DonAntonio I know a little bit about Lie algebras and conformal transformations, but exactly this central extension confuses me. What I am looking for could be something at the level of these BRST lecture notes I could mostly follow. I have not the possibility to aske somebody ind the "real world", and I can neither ask this at physics SE because there any reference / study material questions get immediately closed since some months ... :-/ – Dilaton Apr 3 '13 at 18:00
@Dilaton Central extensions aren't really very hard to understand. They're a lot like direct products, but instead of keeping them completely separated, you allow isomorphic central subgroups of each group to overlap. You should search around for some explanations of central products - they are not difficult, just uncommon. – Alexander Gruber Apr 5 '13 at 5:40
Thanks for this hint @AlexanderGruber, so I will poke around a bit for central procuducts here. – Dilaton Apr 5 '13 at 10:42

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A nice and friendly user at Quora has pointed out these lecture notes to me.

I have not jet fully read it, but is seems very useful to me and obviously explains some additional things I am missing.

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Some more sources (they are actually on string theory, but that clearly means they talk a lot about (super-)virasoro algebra and its applications in physics (specifically string theory) and as a quantisation of Witt Algebra, which is isomorphic to Conformal (AN INTRODUCTION TO STRING THEORY), (Introduction to String Theory), (BUSTEPP LECTURES ON STRING THEORY) – dimensio1n0 Jun 24 '13 at 17:18
Thanks @dimension10 I will look into these too, and the application in ST is what picks me too :-). Too bad, that such questions can no longer be posted on physics SE, where they would fit better. But David Zaslasky would have pounced on it faster than the speed of light and closed it, as soon as he would have seen it if I had tried it at physics SE :-(. So for reference questions on can only ask them here where the moderation is less political and much more reasonable. The drawback of this approach is that such questions get low attention here, because would be better served at physics ... – Dilaton Jun 24 '13 at 17:58
@DImension10AbhimanyuPS I have big troubles, you can read on TRF why ... – Dilaton Aug 25 '13 at 1:57
What?! 4 months?! And David Zaslavasky did that.?, Ok, I'll put that TRF discussion link there . But first, I need to cut 225 characters some how... – dimensio1n0 Aug 25 '13 at 2:15
P.S. Do you intend to return to Physics.SE after the suspension period? Hope you do. – dimensio1n0 Aug 25 '13 at 5:02

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