LECTURES ON HALL ALGEBRAS

By O. Schiffmann. 2006

173 citations recorded by the source corpus.

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)

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/a09619f6d9602591af4c7c1ed3d8943a74e6c6de

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Citations in the corpus

Triangulated Categories: Cluster algebras, quiver representations and triangulated categories (2008, unknown): “Stasheff associahedra [35] [34] [100] [49] [109] [50] ..., • commutative and non commutative algebraic geometry, in particular the study of stability conditions in the sense of Bridgeland [21] [23] [20] [24], Calabi-Yau algebras [72] [36], Donaldson-Thomas invariants [121] [96] [97] [ 99 ] ..., • an”
Decomposition spaces, incidence algebras and Möbius inversion I: Basic theory (2015, background): “Ringel [62]; see also [64], although these sources twist the multiplication by the so-called Euler form).”
Stability conditions and Stokes factors (2008, background): “For a survey of Hall algebras over finite fields see [ 35 ].”