scholarly journals (Contravariant) Koszul Duality for DG Algebras

2013 ◽  
pp. 13-58 ◽  
Author(s):  
Luchezar L. Avramov
Keyword(s):  
Koszul Duality ◽  
Dg Algebras

scholarly journals Blackbox computation of A ∞-algebras

2010 ◽  
Vol 17 (2) ◽  
pp. 391-404
Author(s):  
Mikael Vejdemo-Johansson
Keyword(s):  
Homology Theory ◽  
Algebra Structure ◽  
Finite Amount ◽  
Computational Work ◽  
Dg Algebra ◽  
Dg Algebras

Abstract Kadeishvili's proof of theminimality theorem [T. Kadeishvili, On the homology theory of fiber spaces, Russ. Math. Surv. 35:3 (1980), 231–238] induces an algorithm for the inductive computation of an A ∞-algebra structure on the homology of a dg-algebra. In this paper, we prove that for one class of dg-algebras, the resulting computation will generate a complete A ∞-algebra structure after a finite amount of computational work.

scholarly journals Affine category O, Koszul duality and Zuckerman functors

2021 ◽  
Vol 390 ◽  
pp. 107921
Author(s):  
Ruslan Maksimau
Keyword(s):  
Koszul Duality ◽  
Category O

scholarly journals KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

2010 ◽  
Vol 89 (1) ◽  
pp. 23-49 ◽  
Author(s):  
VOLODYMYR MAZORCHUK
Keyword(s):  
Complete Picture ◽  
Projective Modules ◽  
Koszul Duality ◽  
Tilting Theory

AbstractWe give a complete picture of the interaction between the Koszul and Ringel dualities for graded standardly stratified algebras (in the sense of Cline, Parshall and Scott) admitting linear tilting (co)resolutions of standard and proper costandard modules. We single out a certain class of graded standardly stratified algebras, imposing the condition that standard filtrations of projective modules are finite, and develop a tilting theory for such algebras. Under the assumption on existence of linear tilting (co)resolutions we show that algebras from this class are Koszul, that both the Ringel and Koszul duals belong to the same class, and that these two dualities on this class commute.

Erratum to ?Koszul duality for operads,? vol. 76 (1994) pp. 203?272

1995 ◽  
Vol 80 (1) ◽  
pp. 293-293 ◽  
Author(s):  
V. Ginzburg ◽  
M. Kapranov
Keyword(s):  
Koszul Duality

Koszul Duality I

2020 ◽  
pp. 513-527
Author(s):  
Ben Elias ◽  
Shotaro Makisumi ◽  
Ulrich Thiel ◽  
Geordie Williamson
Keyword(s):  
Koszul Duality

scholarly journals Algorithms in A ∞-algebras

2018 ◽  
Vol 25 (4) ◽  
pp. 629-635
Author(s):  
Mikael Vejdemo-Johansson
Keyword(s):  
Persistent Homology ◽  
Group Cohomology ◽  
Dg Algebras ◽  
Work Done ◽  
Original Theorem

AbstractBased on Kadeishvili’s original theorem inducing{A_{\infty}}-algebra structures on the homology of dg-algebras, several directions of algorithmic research in{A_{\infty}}-algebras have been pursued. In this paper, we survey the work done on calculating explicit{A_{\infty}}-algebra structures from homotopy retractions, in group cohomology and in persistent homology.

Twisted tensor products of DG algebras

2021 ◽  
Vol 76 (6) ◽  
Author(s):  
Dmitri Olegovich Orlov
Keyword(s):  
Tensor Products ◽  
Dg Algebras

Cohomology of g-DG-algebras

1975 ◽  
pp. 93-132
Author(s):  
Franz W. Kamber ◽  
Philippe Tondeur
Keyword(s):  
Dg Algebras
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