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nLab: pentagon relation for the quantum dilogarithm

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  1.  
    • CommentRowNumber1.
    • CommentAuthorjim_stasheff
    • CommentTimeAug 7th 2011
    I think this topic exists within some other entries
    but search has failed.

    I've found lots of papers that refer to
    pentagon relation for the quantum dilogarithm
    but I've yet to find one that states it plain and simple
    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeAug 8th 2011

    quantum dilogarithm has basic references. There is also similar entry dilogarithm.

    • CommentRowNumber3.
    • CommentAuthorjim_stasheff
    • CommentTimeAug 8th 2011
    please name ONE reference which clearly displays the pentagon relation
    • CommentRowNumber4.
    • CommentAuthorzskoda
    • CommentTimeAug 8th 2011
    • (edited Aug 8th 2011)

    Look Jim, do your homework. I have met you first time at Fadell’s birthday conference about 15 years ago. We discussed about a reference of a French thesis relating some CFT physics and Seiberg-Moore procedure/polytopes for CFT and their relation to Grothendieck-Teichmueller tower. You were enthusiastic that I sent you the thesis. But the thesis was in very complicated many file formats and emails were not advanced as now. I had an email which I could use from terminal editor, and it took me about 2 hours to prepare files in sendable formats and send all the files and explanations how to open and use them. Never an answer form you. Ever since I have a feeling of superficiality in every communication we had ever since, kind of at the level of key words. I am sorry but are you seriously trying to make my impression of superficiality more stone-inscribed ?

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 8th 2011

    Gentlemen, if I may:

    I expect that Jim could be away from a suitable university library at present (I got a different query from him offline which suggests this), and he is trying to work with online sources. This might temporarily impinge on his ability to “do homework”.

    Jim, I tried the following method. I went to the nLab page dilogarithm, and in the references clicked on the arXiv article “Dilogarithm identities” by Kirillov. I then did a search in the .pdf file for “pentagon” (using ctrl-F), and the best I could find is on page 82, equation 2.60. Is this what you were looking for?

    It’s none of my business, but the language being used in comment 4 seemed strong, so I was hoping I could be of assistance. One thing though that caught my interest is the mention of the Fadell birthday conference. I believe I was there! Jim had asked whether I might be interested in coming (I was living in Chicago at the time), and I came up for a day. I am sorry that I did not make your acquaintance at the time, Zoran.

    • CommentRowNumber6.
    • CommentAuthorzskoda
    • CommentTimeAug 8th 2011
    • (edited Aug 8th 2011)

    It was his 70th birthday, I believe; I was a graduate student at Wisconsin. Unlike our email proceedings, i should however praise Jim’s excellent, energetic and interesting conference lecture (including the most interesting historical aspect).

    I should emphasize another thing about quantum dilogarithm: Kirillov indeed came to the discovery before Fadeev and Kashaev but recently I heard from someone that there was yet another person involved in early prehistory, but I should check for that fact independently.

    By the way, when mentioning unavailability of references, do you know an online source of the incident between Grothendieck and IHES some 3 years ago or so ? It is possibly relevant for the Grothendieck’s copyright denial in recent email. At the time of the copyright denial I have not known the story which I heard of only recently. Apparently few years ago, Grothendieck wrote a letter to l’IHES requesting a copy of somebody’s (mathematical I guess) preprint from many years ago. Somebody corresponding, possibly a secretary, wrote to him back that they do not copy and deliver publications to arbitrary people, something of the sort. I would like to know the exact story.

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 9th 2011

    Hi Zoran - I would not have the guts to do it, but you could email Luc Illusie; he was the recipient of Grothendieck’s letter (as far as I know) that forbade all further reproduction of G’s work. Or do you know anyone at IHES?

    • CommentRowNumber8.
    • CommentAuthorzskoda
    • CommentTimeAug 9th 2011
    • (edited Aug 9th 2011)

    These are a priori too different events, and roughly a couple of years apart. Illusie is of course not related to l’IHES. Preprint incident was earlier and it is not referred to in the letter to Illusie, but I can imagine if A.G. had a drive to do a little excursion back to mathematics and wanted to do some readings and was denied a key preprint help as an “arbitrary” person and this happened from the institution which is legendary for the connection to him, then I could understand that this could influence the second incident.

    • CommentRowNumber9.
    • CommentAuthorjim_stasheff
    • CommentTimeAug 9th 2011
    @zoran:
    I have met you first time at Fadell's birthday conference about 15 years ago.

    My apologies - my memory failed to make the connection.

    >We discussed about a reference of a French thesis relating some CFT physics and Seiberg-Moore procedure/polytopes for CFT and their relation to Grothendieck-Teichmueller tower. You were enthusiastic that I sent you the thesis. But the thesis was in very complicated many file formats and emails were not advanced as now. I had an email which I could use from terminal editor, and it took me about 2 hours to prepare files in sendable formats and send all the files and explanations how to open and use them. Never an answer form you.

    For that I apologize - NOT my usual style
    Will try to find those files OR is some version of them on the arXiv?
    I hope to have access to mathscinet again by Thursday.

    > Ever since I have a feeling of superficiality in every communication we had ever since, kind of at the level of key words. I am sorry but are you seriously trying to make my impression of superficiality more stone-inscribed ?

    I need to understand the words before I go further - I'm not fluent, for example, in physspeak and only in recent years realized I knew derived cats under another teminology.

    @Todd
    I went to the nLab page dilogarithm, and in the references clicked on the arXiv article "Dilogarithm identities" by Kirillov. I then did a search in the .pdf file for "pentagon" (using ctrl-F), and the best I could find is on page 82, equation 2.60. Is this what you were looking for?

    will check it out - I tried a similar approach with other articles without success

    I was really confused by seeing the Grothedieck thread in this discussion - but now I see how it happened
    • CommentRowNumber10.
    • CommentAuthorjim_stasheff
    • CommentTimeAug 9th 2011
    Todd,
    Yes, eqn 2.60 is the sort of thing I was after
    The Theorem there also pointed out to me that it exists in the context of ab = qba
    so NOT about some version of associativity
    • CommentRowNumber11.
    • CommentAuthorzskoda
    • CommentTimeAug 9th 2011

    Will try to find those files OR is some version of them on the arXiv

    I think not the thesis, but I might dig it in some of the backups from old age…

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