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Derived categories, tilted algebras, and Drinfel'd doubles

✍ Scribed by Liangang Peng; Youjun Tan

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
230 KB
Volume
266
Category
Article
ISSN
0021-8693

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✦ Synopsis

Given a finite dimensional hereditary algebra Ξ› over a finite field k, in the derived category D b (Ξ›) we obtain some formulae on Hall numbers associated to triangles. Using them we prove that, for any tilted algebra Ξ“ of Ξ›, there is an embedding of the twisted Ringel-Hall algebra of Ξ“ into the Drinfel'd double D(Ξ›) of the twisted Ringel-Hall algebra of Ξ›. Furthermore, if Ξ“ is also hereditary, we show that this embedding can be extended as an isomorphism between the two corresponding Drinfel'd doubles. These formulae are also used to construct an automorphism of D(Ξ›) directly associated to Auslander-Reiten translation, and this automorphism follows by B. Sevenhant-M. Van den Bergh's construction in the case of quivers.

πŸ“œ SIMILAR VOLUMES

The character table for a Hopf algebra a
The character table for a Hopf algebra arising from the Drinfel'd double
✍ A. El Alaoui πŸ“‚ Article πŸ“… 2003 πŸ› Elsevier Science 🌐 English βš– 162 KB

In this paper we give a definition of the character table for a Hopf algebra H over a commutative field k of characteristic 0. When H is a finite-dimensional, semisimple, Hopf algebra over an algebraically closed field k of characteristic 0, we obtain a formula for the character table which extends