The Hall algebra of the category of coherent sheaves on the projective line

Details The Hall algebra of the category of coherent sheaves on the projective line The Hall algebra of the category of coherent sheaves on the projective line

1999-06-06

arxiv.org/abs/math/9906037v1

J. reine angew. Math. 533 (2001), 207-233

Mathematics

Quantum Algebra

29 pages

Scientific paper

To an abelian category A of homological dimension 1 satisfying certain finiteness conditions, one can associate an algebra, called the Hall algebra. Kapranov studied this algebra when A is the category of coherent sheaves over a smooth projective curve defined over a finite field, and observed analogies with quantum affine algebras. We recover here in an elementary way his results in the case when the curve is the projective line.

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