[R] 2, Hall-Steinitz-Algebra, pp 3-6; |
[R] 3, Hall-Algebra of a quiver, pp 6-9; |
[R] 3 rest, pp 9-13, Gabriels Theorem, indecomposables and roots; May also look at the notes by Crawley-Boevy http://www.maths.leeds.ac.uk/%7Epmtwc/quivlecs.pdf |
[R] 4.1, pp 14-16, quantum groups; explain a bit more than just generators and relations, say solutions of Yang-Baxter-equation. See also [J]. |
[R] 4.2, pp 16-20, Ringel-Hall-Algebra of Dynkin quiver gives part of quantum group. This was sort of the ignition putting a whole part of mathematics into explosive development. |
[L] Geometric construction of the canonical basis I; This is also in Lusztig's book on quantum groups and in [S2], but I think to concentrate the exposition on the easiest case of a Dynkin quiver might be a good idea. These talks need all of a sudden more technology, namely intersection cohomology and the decomposition theorem. |
[L] Geometric construction of the canonical basis II; |
[S2], Lecture 4.1: Crystals, their tensor product; [J] and Littelmann's overview: Littelmann path model; |
[R] 5, Construction of the enveloping algebra via constructible functions; [S2] Lecture 4.1: Relation to crystals; |
[S1] 4.1-4.3 Hall algebras for coherent sheaves on the projective line I; |
[S1] 4.1-4.3 Hall algebras for coherent sheaves on the projective line II; |
[B] Bridgeland Stability conditions I, and look yourself...; |
[B] Bridgeland Stability conditions II, and look yourself...; |