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.

External links

Introduction to Ringel–Hall algebras

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