On ArXiv there is a new survey paper on finite-dimensional algebras and quivers. The paper is rather dense, so it would be tough going for someone not already familiar with the vocabulary of quivers, but it covers some of the surprising connections with Kac-Moody Lie algebras.

For an easy(ish) to read introduction I recommend the article on quiver representations here.

Good recommendation. That’s much easier to read than the survey article.

I have to say that I find the new registration system for the Notices annoying.

They seem to have lost my account and when I reregistered with the same username it didn’t protest that the account was taken.

Anyway, those AMS articles are great. And I hadn’t met quivers before I found that article a couple of months ago. Surprising how much good stuff comes out of something that at first glance seems like a trivial concept.

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