Daniel Krasner will give the talk on Monday, November 22 at 4:15 in Math 528. This lecture will be open to all.
Abstract: In a paper entitled "Coxeter Functors and Gabriel's Theorem," I.N. Bernstein, I.M. Gelfand, V.A. Ponomarev discuss a uniform way to formulate a range of problems in linear algebra and the relation of these developments to other mathmatics. Namely, they consider the problem of studying linear mappings by looking at representations of directed graphs, where the vertices correspond to finite dimensional vector spaces and edges to linear mappings. Sums and decompositions of representations are defined in the obvious way and the natural question of which graphs, if any, give rise to a finitely many irreducible representations, up to isomorphim. The answer are the Dynkin diagrams, which is Gabriel's theorem. I will give a proof of this result and if time permits discuss some of the implications.
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