Ringel–Hall algebra

In mathematics, a Ringel–Hall algebra is a generalization of the Hall algebra, studied by Ringel (1990). It has a basis of equivalence classes of objects of an abelian category, and the structure constants for this basis are related to the numbers of extensions of objects in the category.

References
  • George Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras. J. Amer. Math. Soc. 4 (1991), no. 2, 365–421.
  • Ringel, Claus Michael (1990), "Hall algebras and quantum groups", Inventiones Mathematicae, 101 (3): 583–591, Bibcode:1990InMat.101..583R, doi:10.1007/BF01231516, MR 1062796
  • Schiffmann, O (2006). "Lectures on Hall algebras". arXiv:math/0611617.
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