Talk:Vertex operator algebra

I don't know what 'clean-uup' is supposed to happen. The article is technical, but not insanitary. Charles Matthews 16:54, 4 November 2005 (UTC)

Problem with example
In the example of a trivial vertex algebra, there is the statement


 * $$\frac{d}{dz} \begin{bmatrix} p-qz & -q \\ q & p-qz \end{bmatrix} =

\begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \begin{bmatrix} p-qz & -q \\ q & p-qz \end{bmatrix} - \begin{bmatrix} p-qz & -q \\ q & p-qz \end{bmatrix} \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix}$$

However, when one calculates both sides one gets:


 * $$ \begin{bmatrix} -q & 0 \\ 0 & -q \end{bmatrix} =

\begin{bmatrix} q & 0 \\ 0 & -q \end{bmatrix} $$

which is not true unless q=0. Nor can I see how to fix this example. Can someone give a reference or explain more details? Wilsonea (talk) 01:17, 20 April 2013 (UTC)

I think you made a mistake. Note there are two minuses in the second term making a plus. So the example is fine. (PB)

which John Conway?
I'm guessing John B. Conway. Someone who knows, please dab the link. --Trovatore 07:53, 28 November 2005 (UTC)
 * Whoops, guess it's John H. after all. (Followed the Borcherds link) --Trovatore 07:54, 28 November 2005 (UTC)

Definition problem
In the four point function axiom it refers to Y(Y(a,z-w)b,w)c which doesn't appear to make sense. Y(a,z-w)b, which is a Laurent series in z-w, cannot be used as the first argument of Y; only elements of V fit in the first argument slot of Y. (Unless we have somehow silently extended Y to a map on V((z-w)).) AxelBoldt (talk) 20:38, 5 April 2009 (UTC)


 * Y is silently extended to a map on V((z-w)). Incidentally, this definition is not the weakest possible, since one only needs two of the series to be equal to derive equality of the third.  Also, it may be more correct to call it a two-point function axiom, since one is inserting the vacuum at the other two points.  --S.H.C.  —Preceding unsigned comment added by 18.87.1.212 (talk) 02:48, 7 April 2009 (UTC)

Motivation for VOA
Recently, Richard Borcherds has posted on MathOverflow about the original motivation for the definition of VOA. Someone with some expertise might want to edit the article accordingly. Akriasas (talk) 08:35, 13 February 2011 (UTC)


 * I have made a correction — Preceding unsigned comment added by 150.203.115.105 (talk) 05:17, 22 January 2014 (UTC)

Checking Examples
Someone should check the examples as they don't seem to be correct. —Preceding unsigned comment added by 86.135.196.242 (talk) 21:37, 31 March 2011 (UTC)
 * They are transcribed from the book of Victor Kac and you are probably an ipsock of A.K.Nole. Mathsci (talk) 21:53, 31 March 2011 (UTC)

Checking by Expert
The examples seem to be fixed now and add to the clarity but the whole article could do with going over by an expert and tidying up. But without making it too abstract so that non-experts can still understand it. —Preceding unsigned comment added by 86.174.105.219 (talk) 17:39, 8 May 2011 (UTC)
 * I think this is on the watchlist of an expert. The statement you made in the Monster example about the naming of vertex algebras does not seem correct, but that can be sorted out in due course. Mathsci (talk) 19:13, 8 May 2011 (UTC)

References for the "Additional constructions" section?
Could some references be added in Additional constructions? There are five very significant constructions listed, and only in the fourth item (the coset construction) it is mentioned that this construction is due to Goddard, Kent and Olive; no actual reference is given even there. 109.172.129.12 (talk) 15:24, 25 January 2019 (UTC)

Bloated lede
I think the lede is a little bloated and overly technical. Any experts agree and are willing to do a bit of cleanup there? Zephyr the west wind (talk) 22:06, 9 August 2023 (UTC)