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equivocate algebras – Reference request: a story of two mathematicians Answer

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equivocate algebras – Reference request: a story of two mathematicians

I heard the next anecdote with Pierre Gabriel and Jacques Tits no less than twice in a 4 yr or so:

When Fr. Gabriel offered the concept in a convention [sometime around 1970]He stated one thing love this, “OK, this algebra is of the finite representation type; so the algebra has a linear quiver and you get it $ n + 1 $ indivisible modules (in the case $ A_ {n} $). In the event of $ D_ {n} $, They have [an exact expression depending on $n$] indivisible modules. There are exceptional cases $ E_ {6}, E_ {7} $, and $ E_ {8} $“. He beforehand talked about the variety of modules that can’t breathe dismantled $ E_ {6} $somebody in his viewers stated the rectify quantity aloud. Again, earlier than he counts the variety of indecomposable modules within the illustration of. talked about $ E_ {7} $, the identical individual within the viewers gave the rectify quantity. This status precipitated Fr. Gabriel to question: “Who is answering?” As it turned out, that individual was J. Tits. When Fr. Gabriel requested him if he already knew the sentence, J. Tits replied: “No, I don’t know. I only gave the number of roots of the Lie algebra that is assigned to the corresponding Dynkin diagram. “. .. What was the connection between the indecomposable modules on algebras and the roots of Lie algebras? The respond was not very limpid on the time …

Even if the earlier recast of the story might breathe a bit mistaken (I heard it (roughly) love this at a convention of Professor JA de la Peña in 2017), does anybody know whether or not such an trade between Fr. Gabriel and J. Tits really occurred? If so, would you breathe so kindly as to supply probably the most correct model of it that you’re cognizant of or, if not, some reference to the literature the place a extra circumstantial narrative of this story can breathe create?

Thank you in forward to your consideration and competent solutions.

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