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Minimal Generators of Ringel–Hall Algebras of Affine Quivers

✍ Scribed by Pu Zhang; Ying-Bo Zhang; Jin-Yun Guo


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
198 KB
Volume
239
Category
Article
ISSN
0021-8693

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✦ Synopsis


Let H H kQ be the Ringel᎐Hall algebra of affine quiver Q. All indecomposable Ž . representations of Q, which can be generated inside H H kQ by ''smaller'' represen-Ž . tations of Q, are classified; systems of minimal homogeneous generators of H H kQ are explicitly written out.


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On the Double of the Hall Algebra of a Q
✍ Bert Sevenhant; Michel Van den Bergh 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 181 KB

We show that it is possible to define reflection isomorphisms on the double of the (twisted) Hall algebra of a quiver. Combining these reflections with Fourier transform yields an alternative construction of Lusztig's braid group action on a quantum enveloping algebra.