科研之友
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摘要
Let coh X be the category of coherent sheaves over a weighted projective line X and let D-b (coh X) be its bounded derived category. The present paper focuses on the study of the right and left mutation functors arising in D-b (coh X) attached to certain line bundles. As applications, we first show that these mutation functors give rise to simple reflections for the Weyl group of the star-shaped quiver Q associated with X. By further dealing with the Ringel-Hall algebra of X, we show that these functors provide a realization for Tits' automorphisms of the Kac-Moody algebra g(Q) associated with Q, as well as for Lusztig's symmetries of the quantum enveloping algebra of g(Q).
