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.
The Double Ringel-Hall Algebras of Valued Quivers*
✍ Scribed by Yanxin Wang; Jie Xiao
- Publisher
- Coastal and Estuarine Research Federation
- Year
- 2006
- Tongue
- English
- Weight
- 302 KB
- Volume
- 27
- Category
- Article
- ISSN
- 1860-6261
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📜 SIMILAR VOLUMES
As a continuation of the work of Ringel and Green on Hall algebras, the Hopf Ž . algebra structure of a extended twisted Hall algebra is presented here. By introducing the Ringel pairing of Hall algebras, the Drinfeld double of a Hall algebra is constructed. The reduced form of this Drinfeld double
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.