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Drinfeld Double and Ringel–Green Theory of Hall Algebras

✍ Scribed by Jie Xiao

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
530 KB
Volume
190
Category
Article
ISSN
0021-8693

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✦ Synopsis

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 is applicable to the generic composition algebra, which gives a complete realization of quantum group. This Ringel᎐Green theory makes it possible to give the formulae for the computation of commutators in quantum groups in terms of Hall algebras.

📜 SIMILAR VOLUMES

Twisted Hopf Algebras, Ringel–Hall Algeb
Twisted Hopf Algebras, Ringel–Hall Algebras, and Green's Categories: With an appendix by the referee
✍ Libin Li; Pu Zhang 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 215 KB

The concept and some basic properties of a twisted Hopf algebra are introduced and investigated. Its unique difference from a Hopf algebra is that the comultiplication ␦ : A ª A m A is an algebra homomorphism, not for the componentwise multiplication on A m A, but for the twisted multiplication on A