Koszul Equivalences in $A_\infty$-Algebras
| dc.creator | Lu, D. -M. | |
| dc.creator | Palmieri, J. H. | |
| dc.creator | Wu, Q. -S. | |
| dc.creator | Zhang, J. J. | |
| dc.date | 2007-10-29 | |
| dc.date.accessioned | 2026-07-07T08:39:15Z | |
| dc.date.available | 2026-07-07T08:39:15Z | |
| dc.description | We prove a version of Koszul duality and the induced derived equivalence for Adams connected $A_\infty$-algebras that generalizes the classical Beilinson-Ginzburg-Soergel Koszul duality. As an immediate consequence, we give a version of the Bernšte{\uı}n-Gel'fand-Gel'fand correspondence for Adams connected $A_\infty$-algebras. We give various applications. For example, a connected graded algebra $A$ is Artin-Schelter regular if and only if its Ext-algebra $\Ext^\ast_A(k,k)$ is Frobenius. This generalizes a result of Smith in the Koszul case. If $A$ is Koszul and if both $A$ and its Koszul dual $A^!$ are noetherian satisfying a polynomial identity, then $A$ is Gorenstein if and only if $A^!$ is. The last statement implies that a certain Calabi-Yau property is preserved under Koszul duality. | |
| dc.identifier | https://arxiv.org/abs/0710.5492 | |
| dc.identifier | http://arxiv.org/abs/0710.5492 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141010 | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16A03; 16A62; 16E65 | |
| dc.title | Koszul Equivalences in $A_\infty$-Algebras | |
| dc.type | text |