Derived Picard Groups of Finite Dimensional Hereditary Algebras
| dc.creator | Miyachi, Jun-ichi | |
| dc.creator | Yekutieli, Amnon | |
| dc.date | 1999-04-02 | |
| dc.date | 2000-10-25 | |
| dc.date.accessioned | 2026-07-07T05:28:35Z | |
| dc.date.available | 2026-07-07T05:28:35Z | |
| dc.description | Let A be an algebra over a field k, and denote by D^b(Mod A) the bounded derived category of left A-modules. The derived Picard group DPic_k(A) is the group of triangle auto-equivalences of D^b(Mod A) induced by tilting complexes. We study the group DPic_k(A) when A = k Δis the path algebra of a finite quiver Δ. We obtain general results on the structure of DPic_k(A), as well as explicit calculations for many cases, including all finite and tame representation types. Our method is to construct a representation of DPic_k(A) on a certain infinite quiver. This representation is faithful whenΔis a tree, and then DPic_k(A) is discrete. Otherwise a connected linear algebraic group can occur as a factor of DPic_k(A). When A is hereditary, DPic_k(A) coincides with the full group of k-linear triangle auto-equivalences of D^b(Mod} A). Hence we can calculate the group of such auto-equivalences for any triangulated category D equivalent to D^b(Mod A). These include the derived categories of certain noncommutative spaces introduced by Kontsevich-Rosenberg. | |
| dc.description | 24 pages, AMSLaTeX with 6 encapsulated postscript figures, some errors corrected, introductory material edited, to appear in Compositio Math | |
| dc.identifier | https://arxiv.org/abs/math/9904006 | |
| dc.identifier | http://arxiv.org/abs/math/9904006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78314 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Representation Theory | |
| dc.subject | 18E30, 16G20; 16G70, 16G60, 16E20, 14C22 | |
| dc.title | Derived Picard Groups of Finite Dimensional Hereditary Algebras | |
| dc.type | text |