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In mathematics, a Ringel–Hall algebra is a generalization of the Hall algebra, studied by Claus Michael 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
edit- Lusztig, George (1991), "Quivers, perverse sheaves, and quantized enveloping algebras", Journal of the American Mathematical Society, 4 (2): 365–421, CiteSeerX 10.1.1.454.3334, doi:10.1090/S0894-0347-1991-1088333-2, JSTOR 2939279, MR 1088333
- 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, S2CID 120480847
- Schiffmann, Olivier (2006). "Lectures on Hall algebras". arXiv:math/0611617.
External links
edit- Hubery, Andrew W., Introduction to Ringel–Hall algebras (PDF), Bielefeld University