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Lectures on Hall algebras

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arxiv math/0611617 v2 pith:5EL22LWM submitted 2006-11-20 math.RT math.QA

Olivier Schiffmann This is my paper · ORCID
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These are notes for a minicourse on Hall algebras given at the ICTP in Trieste in January 2006. After giving the definition and first properties of Hall algebras, we study in some details the classical Hall algebra, the Hall algebra of quivers, and the Hall algebra of coherent sheaves on smooth projective curves. The last section deals with the Hall algebras in the context of derived categories. (The figures only seem to come out nicely in the .ps file)

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Cited by 3 Pith papers

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  1. Proto-Exact Categories of Matroids over Idylls and Tropical Toric Reflexive Sheaves

    math.CT 2025-09 conditional novelty 6.0 of 10

    The authors prove that pointed matroids over perfect idylls form a combinatorial proto-exact category with duality and exact direct sum, and that tropical toric reflexive sheaves (modular ones in particular) are proto...

  2. Quiver Schur algebras and cohomological Hall algebras

    math.RT 2019-07 unverdicted novelty 6.0 of 10

    Quiver Schur algebras are realized as operator algebras on cohomological Hall algebras, with shuffle descriptions reinterpreted using Demazure operators, plus results on mixed versions and geometric realizations of mo...

  3. Hall Geometry and Auslander-Reiten Quiver

    math.AG 2026-06 unverdicted novelty 5.0 of 10

    Motivic Hall algebra geometry and moduli stack correspondences recover Auslander-Reiten sequences and the Auslander-Reiten quiver.

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