A Survey on Koszul Algebras and Koszul Duality

Leavitt Path Algebras and Classical K-Theory - Indian Statistical Institute Series ◽

10.1007/978-981-15-1611-5_7 ◽

2020 ◽

pp. 157-176

Author(s):

Neeraj Kumar

Keyword(s):

Koszul Algebras ◽

Koszul Duality

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Koszul duality for N-Koszul algebras

Colloquium Mathematicum ◽

10.4064/cm103-2-1 ◽

2005 ◽

Vol 103 (2) ◽

pp. 155-168 ◽

Cited By ~ 1

Author(s):

Roberto Martínez-Villa ◽

Manuel Saorín

Keyword(s):

Koszul Algebras ◽

Koszul Duality

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Homogeneous Vector Bundles and Koszul Algebras

Mathematische Nachrichten ◽

10.1002/mana.19981910109 ◽

1998 ◽

Vol 191 (1) ◽

pp. 189-195 ◽

Cited By ~ 5

Author(s):

Lutz Hille

Keyword(s):

Vector Bundles ◽

Koszul Algebras ◽

Homogeneous Vector

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Affine category O, Koszul duality and Zuckerman functors

Advances in Mathematics ◽

10.1016/j.aim.2021.107921 ◽

2021 ◽

Vol 390 ◽

pp. 107921

Author(s):

Ruslan Maksimau

Keyword(s):

Koszul Duality ◽

Category O

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Koszul algebras and flow lattices

Journal of Combinatorial Theory Series A ◽

10.1016/j.jcta.2021.105534 ◽

2022 ◽

Vol 185 ◽

pp. 105534

Author(s):

Zsuzsanna Dancso ◽

Anthony M. Licata

Keyword(s):

Koszul Algebras

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Koszul Algebras and Their Ideals

Functional Analysis and Its Applications ◽

10.1007/s10688-005-0024-6 ◽

2005 ◽

Vol 39 (2) ◽

pp. 120-130 ◽

Cited By ~ 2

Author(s):

D. I. Piontkovskii

Keyword(s):

Koszul Algebras

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KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788710001497 ◽

2010 ◽

Vol 89 (1) ◽

pp. 23-49 ◽

Cited By ~ 9

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.

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