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Journal articles on the topic 'Koszul duality in Galois theory'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Positselski, Leonid, and Alexander Vishik. "Koszul duality and Galois cohomology." Mathematical Research Letters 2, no. 6 (1995): 771–81. http://dx.doi.org/10.4310/mrl.1995.v2.n6.a8.

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2

Hirsh, Joseph, and Joan Millès. "Curved Koszul duality theory." Mathematische Annalen 354, no. 4 (2012): 1465–520. http://dx.doi.org/10.1007/s00208-011-0766-9.

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3

Mirković, Ivan, and Simon Riche. "Linear Koszul duality." Compositio Mathematica 146, no. 1 (2009): 233–58. http://dx.doi.org/10.1112/s0010437x09004357.

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AbstractIn this paper we construct, for F1 and F2 subbundles of a vector bundle E, a ‘Koszul duality’ equivalence between derived categories of 𝔾m-equivariant coherent(dg-)sheaves on the derived intersection $F_1 \rcap _E F_2$, and the corresponding derived intersection $F_1^{\perp } \rcap _{E^*} F_2^{\perp }$. We also propose applications to Hecke algebras.

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4

Riche, Simon, Wolfgang Soergel, and Geordie Williamson. "Modular Koszul duality." Compositio Mathematica 150, no. 2 (2013): 273–332. http://dx.doi.org/10.1112/s0010437x13007483.

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AbstractWe prove an analogue of Koszul duality for category$ \mathcal{O} $of a reductive group$G$in positive characteristic$\ell $larger than$1$plus the number of roots of$G$. However, there are no Koszul rings, and we do not prove an analogue of the Kazhdan–Lusztig conjectures in this context. The main technical result is the formality of the dg-algebra of extensions of parity sheaves on the flag variety if the characteristic of the coefficients is at least the number of roots of$G$plus$2$.

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5

Chuang, Joseph, Andrey Lazarev, and Wajid Mannan. "Koszul–Morita duality." Journal of Noncommutative Geometry 10, no. 4 (2016): 1541–57. http://dx.doi.org/10.4171/jncg/265.

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6

Beilinson, Alexander, Victor Ginzburg, and Wolfgang Soergel. "Koszul Duality Patterns in Representation Theory." Journal of the American Mathematical Society 9, no. 2 (1996): 473–527. http://dx.doi.org/10.1090/s0894-0347-96-00192-0.

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7

Etgü, Tolga, and Yankı Lekili. "Koszul duality patterns in Floer theory." Geometry & Topology 21, no. 6 (2017): 3313–89. http://dx.doi.org/10.2140/gt.2017.21.3313.

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8

Paquette, Natalie M., and Brian R. Williams. "Koszul duality in quantum field theory." Confluentes Mathematici 14, no. 2 (2023): 87–138. http://dx.doi.org/10.5802/cml.88.

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9

DOTSENKO, VLADIMIR, and BRUNO VALLETTE. "HIGHER KOSZUL DUALITY FOR ASSOCIATIVE ALGEBRAS." Glasgow Mathematical Journal 55, A (2013): 55–74. http://dx.doi.org/10.1017/s0017089513000505.

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AbstractWe present a unifying framework for the key concepts and results of higher Koszul duality theory for N-homogeneous algebras: the Koszul complex, the candidate for the space of syzygies and the higher operations on the Yoneda algebra. We give a universal description of the Koszul dual algebra under a new algebraic structure. For that we introduce a general notion: Gröbner bases for algebras over non-symmetric operads.

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10

Tu, Junwu. "Matrix factorizations via Koszul duality." Compositio Mathematica 150, no. 9 (2014): 1549–78. http://dx.doi.org/10.1112/s0010437x14007295.

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AbstractIn this paper we prove a version of curved Koszul duality for $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\mathbb{Z}/2\mathbb{Z}$-graded curved coalgebras and their cobar differential graded algebras. A curved version of the homological perturbation lemma is also obtained as a useful technical tool for studying curved (co)algebras and precomplexes. The results of Koszul duality can be applied to study the category of m

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11

Bodzenta, Agnieszka, and Julian Külshammer. "Ringel duality as an instance of Koszul duality." Journal of Algebra 506 (July 2018): 129–87. http://dx.doi.org/10.1016/j.jalgebra.2018.03.025.

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12

Chuang, Joseph, Andrey Lazarev, and W. H. Mannan. "Cocommutative coalgebras: homotopy theory and Koszul duality." Homology, Homotopy and Applications 18, no. 2 (2016): 303–36. http://dx.doi.org/10.4310/hha.2016.v18.n2.a17.

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13

MAZORCHUK, VOLODYMYR. "KOSZUL DUALITY FOR STRATIFIED ALGEBRAS II. STANDARDLY STRATIFIED ALGEBRAS." Journal of the Australian Mathematical Society 89, no. 1 (2010): 23–49. http://dx.doi.org/10.1017/s1446788710001497.

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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 R

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14

Bellier, Olivia. "Koszul duality theory for operads over Hopf algebras." Algebraic & Geometric Topology 14, no. 1 (2014): 1–35. http://dx.doi.org/10.2140/agt.2014.14.1.

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15

Krause, Henning. "Koszul, Ringel and Serre duality for strict polynomial functors." Compositio Mathematica 149, no. 6 (2013): 996–1018. http://dx.doi.org/10.1112/s0010437x12000814.

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AbstractThis is a report on recent work of Chałupnik and Touzé. We explain the Koszul duality for the category of strict polynomial functors and make explicit the underlying monoidal structure which seems to be of independent interest. Then we connect this to Ringel duality for Schur algebras and describe Serre duality for strict polynomial functors.

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16

Calaque, Damien, Giovanni Felder, Andrea Ferrario, and Carlo A. Rossi. "Bimodules and branes in deformation quantization." Compositio Mathematica 147, no. 1 (2010): 105–60. http://dx.doi.org/10.1112/s0010437x10004847.

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AbstractWe prove a version of Kontsevich’s formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X*) and ∧(X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet’s recent paper on Koszul duality in deformation quantization.

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17

Madsen, Dag Oskar. "Quasi-hereditary algebras and generalized Koszul duality." Journal of Algebra 395 (December 2013): 96–110. http://dx.doi.org/10.1016/j.jalgebra.2013.08.005.

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18

Martínez-Villa, Roberto, and Manuel Saorín. "A duality theorem for generalized Koszul algebras." Journal of Algebra 315, no. 1 (2007): 121–33. http://dx.doi.org/10.1016/j.jalgebra.2006.05.041.

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19

Maunder, James. "Koszul duality and homotopy theory of curved Lie algebras." Homology, Homotopy and Applications 19, no. 1 (2017): 319–40. http://dx.doi.org/10.4310/hha.2017.v19.n1.a16.

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20

Drozd, Yuriy, and Volodymyr Mazorchuk. "Koszul duality for extension algebras of standard modules." Journal of Pure and Applied Algebra 211, no. 2 (2007): 484–96. http://dx.doi.org/10.1016/j.jpaa.2007.01.014.

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21

Medvedev, Alice, and Ramin Takloo-Bighash. "An Invitation to Model-Theoretic Galois Theory." Bulletin of Symbolic Logic 16, no. 2 (2010): 261–69. http://dx.doi.org/10.2178/bsl/1286889126.

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AbstractWe carry out some of Galois' work in the setting of an arbitrary first-order theory T. We replace the ambient algebraically closed field by a large model M of T, replace fields by definably closed subsets of M, assume that T codes finite sets, and obtain the fundamental duality of Galois theory matching subgroups of the Galois group of L over F with intermediate extensions F ≤ K ≤ L. This exposition of a special case of [10] has the advantage of requiring almost no background beyond familiarity with fields, polynomials, first-order formulae, and automorphisms.

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22

Villa, Roberto Martínez, and Alex Martsinkovsky. "Stable Projective Homotopy Theory of Modules, Tails, and Koszul Duality." Communications in Algebra 38, no. 10 (2010): 3941–73. http://dx.doi.org/10.1080/00927870903339980.

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23

DAVEY, BRIAN A., JANE G. PITKETHLY, and ROSS WILLARD. "THE LATTICE OF ALTER EGOS." International Journal of Algebra and Computation 22, no. 01 (2012): 1250007. http://dx.doi.org/10.1142/s021819671100673x.

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We introduce a new Galois connection for partial operations on a finite set, which induces a natural quasi-order on the collection of all partial algebras on this set. The quasi-order is compatible with the basic concepts of natural duality theory, and we use it to turn the set of all alter egos of a given finite algebra into a doubly algebraic lattice. The Galois connection provides a framework for us to develop further the theory of natural dualities for partial algebras. The development unifies several fundamental concepts from duality theory and reveals a new understanding of full dualitie

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24

Chen, Xiaojun, Youming Chen, Farkhod Eshmatov, and Song Yang. "Poisson cohomology, Koszul duality, and Batalin–Vilkovisky algebras." Journal of Noncommutative Geometry 15, no. 3 (2021): 889–918. http://dx.doi.org/10.4171/jncg/425.

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25

MONJARDET, BERNARD. "SOME ORDER DUALITIES IN LOGIC, GAMES AND CHOICES." International Game Theory Review 09, no. 01 (2007): 1–12. http://dx.doi.org/10.1142/s0219198907001242.

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We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then, we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally, we present two "concrete" dualities occuring in social choice and in choice functions theories.

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26

Masuoka, Akira, and Tadashi Yanai. "Hopf module duality applied to X-outer Galois theory." Journal of Algebra 265, no. 1 (2003): 229–46. http://dx.doi.org/10.1016/s0021-8693(03)00130-3.

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27

Batanin, Michael, and Martin Markl. "Operadic categories as a natural environment for Koszul duality." Compositionality 5 (June 5, 2023): 3. http://dx.doi.org/10.32408/compositionality-5-3.

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This is the first paper of a series which aims to set up the cornerstones of Koszul duality for operads over operadic categories. To this end we single out additional properties of operadic categories under which the theory of quadratic operads and their Koszulity can be developed, parallel to the traditional one by Ginzburg–Kapranov. We then investigate how these extra properties interact with discrete operadic (op)fibrations, which we use as a powerful tool to construct new operadic categories from old ones. We pay particular attention to the operadic category of graphs, giving a full descri

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28

Dascalescu, S., S. Raianu, and Y. H. Zhang. "Finite Hopf-Galois Coextensions, Crossed Coproducts, and Duality." Journal of Algebra 178, no. 2 (1995): 400–413. http://dx.doi.org/10.1006/jabr.1995.1356.

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29

Blumberg, Andrew J., and Michael A. Mandell. "Derived Koszul duality and involutions in the algebraic K -theory of spaces." Journal of Topology 4, no. 2 (2011): 327–42. http://dx.doi.org/10.1112/jtopol/jtr003.

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30

Idrissi, Najib. "Curved Koszul duality of algebras over unital versions of binary operads." Journal of Pure and Applied Algebra 227, no. 3 (2023): 107208. http://dx.doi.org/10.1016/j.jpaa.2022.107208.

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31

Guan, Ai, and Andrey Lazarev. "Koszul duality for compactly generated derived categories of second kind." Journal of Noncommutative Geometry 15, no. 4 (2021): 1355–71. http://dx.doi.org/10.4171/jncg/438.

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32

Gazaki, Evangelia. "A finer Tate duality theorem for local Galois symbols." Journal of Algebra 509 (September 2018): 337–85. http://dx.doi.org/10.1016/j.jalgebra.2018.05.007.

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33

Marti´nez Villa, Roberto, and Alex Martsinkovsky. "Cohomology of tails, Tate–Vogel cohomology, and noncommutative Serre duality over Koszul quiver algebras." Journal of Algebra 280, no. 1 (2004): 58–83. http://dx.doi.org/10.1016/j.jalgebra.2004.05.017.

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34

Omprakash, Atale. "Galois connections and isomorphism of simultaneous ordered relations." Annals of Communications in Mathematics 6, no. 2 (2023): 109–17. https://doi.org/10.5281/zenodo.10059526.

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In order theory, partially ordered sets are only equipped with one relation which decides the entire structure/Hasse diagram of the set. In this paper we have presented how partially ordered sets can be studied under simultaneous partially ordered relations which we have called binary posets. The paper is motivated by the problem of operating a set simultaneously under two distinct partially ordered relations. It has been shown that binary posets follow duality principle just like posets do. Within this framework, some new definitions concerning maximal and minimal elements are also presented.

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35

Stalder, Nicolas. "The semisimplicity conjecture for A-motives." Compositio Mathematica 146, no. 3 (2010): 561–98. http://dx.doi.org/10.1112/s0010437x09004448.

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AbstractWe prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V𝔭(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of K. This theorem is in analogy with known results for abelian varieties and Drinfeld modules, and has been sketched previously by Tamagawa. We deduce two consequences of the theorem for the algebraic monodromy groups G𝔭(M) associated to an A-motive M by Tannakian duality. The first requires no semisimplicity condition on M and states that G𝔭(M) may be

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36

Gazaki, Evangelia. "A Tate duality theorem for local Galois symbols II; The semi-abelian case." Journal of Number Theory 204 (November 2019): 532–60. http://dx.doi.org/10.1016/j.jnt.2019.04.017.

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37

Cais, Bryden. "The geometry of Hida families II: -adic -modules and -adic Hodge theory." Compositio Mathematica 154, no. 4 (2018): 719–60. http://dx.doi.org/10.1112/s0010437x17007680.

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We construct the $\unicode[STIX]{x1D6EC}$-adic crystalline and Dieudonné analogues of Hida’s ordinary $\unicode[STIX]{x1D6EC}$-adic étale cohomology, and employ integral $p$-adic Hodge theory to prove $\unicode[STIX]{x1D6EC}$-adic comparison isomorphisms between these cohomologies and the $\unicode[STIX]{x1D6EC}$-adic de Rham cohomology studied in Cais [The geometry of Hida families I:$\unicode[STIX]{x1D6EC}$-adic de Rham cohomology, Math. Ann. (2017), doi:10.1007/s00208-017-1608-1] as well as Hida’s $\unicode[STIX]{x1D6EC}$-adic étale cohomology. As applications of our work, we provide a ‘coh

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38

Yamashita, Hiroshi. "On the rank of the first radical layer of a p-class group of an algebraic number field." Nagoya Mathematical Journal 156 (1999): 85–108. http://dx.doi.org/10.1017/s0027763000007078.

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Let p be a prime number. Let M be a finite Galois extension of a finite algebraic number field k. Suppose that M contains a primitive pth root of unity and that the p-Sylow subgroup of the Galois group G = Gal(M/k) is normal. Let K be the intermediate field corresponding to the p-Sylow subgroup. Let = Gal(K/k). The p-class group C of M is a module over the group ring ZpG, where Zp is the ring of p-adic integers. Let J be the Jacobson radical of ZpG. C/JC is a module over a semisimple artinian ring Fp. We study multiplicity of an irreducible representation Φ apperaring in C/JC and prove a formu

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39

Gehrmann, Lennart, and Giovanni Rosso. "Big principal series, -adic families and -invariants." Compositio Mathematica 158, no. 2 (2022): 409–36. http://dx.doi.org/10.1112/s0010437x2200731x.

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In earlier work, the first named author generalized the construction of Darmon-style $\mathcal {L}$ -invariants to cuspidal automorphic representations of semisimple groups of higher rank, which are cohomological with respect to the trivial coefficient system and Steinberg at a fixed prime. In this paper, assuming that the Archimedean component of the group has discrete series we show that these automorphic $\mathcal {L}$ -invariants can be computed in terms of derivatives of Hecke eigenvalues in $p$ -adic families. Our proof is novel even in the case of modular forms, which was established by

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40

DAVID, MARIE-CLAUDE, and NICOLAS M. THIÉRY. "EXPLORATION OF FINITE-DIMENSIONAL KAC ALGEBRAS AND LATTICES OF INTERMEDIATE SUBFACTORS OF IRREDUCIBLE INCLUSIONS." Journal of Algebra and Its Applications 10, no. 05 (2011): 995–1106. http://dx.doi.org/10.1142/s0219498811005099.

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We study the four infinite families KA(n), KB(n), KD(n), and KQ(n) of finite-dimensional Hopf (in fact Kac) algebras constructed, respectively, by A. Masuoka and L. Vainerman: isomorphisms, automorphism groups, self-duality, lattices of coideal sub-algebras. We reduce the study to KD(n) by proving that the others are isomorphic to KD(n), its dual, or an index 2 subalgebra of KD(2n). We derive many examples of lattices of intermediate subfactors of the inclusions of depth 2 associated to those Kac algebras, as well as the corresponding principal graphs, which is the original motivation. Along t

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41

Francis, John. "The tangent complex and Hochschild cohomology of -rings." Compositio Mathematica 149, no. 3 (2012): 430–80. http://dx.doi.org/10.1112/s0010437x12000140.

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AbstractIn this work, we study the deformation theory of${\mathcal {E}}_n$-rings and the${\mathcal {E}}_n$analogue of the tangent complex, or topological André–Quillen cohomology. We prove a generalization of a conjecture of Kontsevich, that there is a fiber sequence$A[n-1] \rightarrow T_A\rightarrow {\mathrm {HH}}^*_{{\mathcal {E}}_{n}}\!(A)[n]$, relating the${\mathcal {E}}_n$-tangent complex and${\mathcal {E}}_n$-Hochschild cohomology of an${\mathcal {E}}_n$-ring$A$. We give two proofs: the first is direct, reducing the problem to certain stable splittings of configuration spaces of puncture

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42

Li, Haonan, and Quanshui Wu. "Generalized Koszul Algebra and Koszul Duality." Journal of Algebra, December 2022. http://dx.doi.org/10.1016/j.jalgebra.2022.12.023.

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43

Hirsh, Joseph, and Joan Millès. "Correction to: Curved Koszul duality theory." Mathematische Annalen, June 27, 2023. http://dx.doi.org/10.1007/s00208-023-02635-5.

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44

Cassella, Alberto, and Claudio Quadrelli. "Right-angled Artin groups and enhanced Koszul properties." Journal of Group Theory, August 25, 2020. http://dx.doi.org/10.1515/jgth-2020-0049.

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AbstractLet 𝔽 be a finite field. We prove that the cohomology algebra H^{\bullet}(G_{\Gamma},\mathbb{F}) with coefficients in 𝔽 of a right-angled Artin group G_{\Gamma} is a strongly Koszul algebra for every finite graph Γ. Moreover, H^{\bullet}(G_{\Gamma},\mathbb{F}) is a universally Koszul algebra if, and only if, the graph Γ associated to the group G_{\Gamma} has the diagonal property. From this, we obtain several new examples of pro-𝑝 groups, for a prime number 𝑝, whose continuous cochain cohomology algebra with coefficients in the field of 𝑝 elements is strongly and universally (or strong

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45

Ayala, David, and John Francis. "ZERO-POINTED MANIFOLDS." Journal of the Institute of Mathematics of Jussieu, July 2, 2019, 1–74. http://dx.doi.org/10.1017/s1474748019000343.

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We formulate a theory of pointed manifolds, accommodating both embeddings and Pontryagin–Thom collapse maps, so as to present a common generalization of Poincaré duality in topology and Koszul duality in${\mathcal{E}}_{n}$-algebra.

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46

Savage, Rhiannon. "Koszul Monoids in Quasi-abelian Categories." Applied Categorical Structures 31, no. 6 (2023). http://dx.doi.org/10.1007/s10485-023-09756-7.

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AbstractSuppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $$\mathcal {E}$$ E with enough flat projectives, such as the category of complete bornological spaces $${{\textbf {CBorn}}}_k$$ CBorn k or the category of inductive limits of Banach spaces $${{\textbf {IndBan}}}_k$$ IndBan k . Working with monoids in $$\mathcal {E}$$ E , we can generalise and extend the Koszul duality theory of Beilinson, Ginzburg, Soergel. We use an element-free approach to define the notions of Koszul monoids, and quadratic monoids and their duals. Schneiders’ embedding of a quasi-abel

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47

Fernández, Víctor E. "One-loop corrections to the celestial chiral algebra from Koszul Duality." Journal of High Energy Physics 2023, no. 4 (2023). http://dx.doi.org/10.1007/jhep04(2023)124.

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Abstract We consider self-dual Yang-Mills theory (SDYM) in four dimensions and its lift to holomorphic BF theory on twistor space. Following the work of Costello and Paquette, we couple SDYM to a quartic axion field, which guarantees associativity of the (extended) celestial chiral algebra at the quantum level. We demonstrate how to reproduce their one-loop quantum deformation to the chiral algebra using Koszul duality.

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48

Hartonas, Chrysafis. "Duality for normal lattice expansions and sorted residuated frames with relations." Algebra universalis 84, no. 1 (2023). http://dx.doi.org/10.1007/s00012-023-00802-y.

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AbstractWe revisit the problem of Stone duality for lattices with quasioperators, presenting a fresh duality result. The new result is an improvement over that of our previous work in two important respects. First, the axiomatization of frames is now simplified, partly by incorporating Gehrke’s proposal of section stability for relations. Second, morphisms are redefined so as to preserve Galois stable (and co-stable) sets and we rely for this, partly again, on Goldblatt’s recently proposed definition of bounded morphisms for polarities. In studying the dual algebraic structures associated to p

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49

Asensouyis, Hassan, Jilali Assim, Zouhair Boughadi, and Youness Mazigh. "Poitou–Tate duality for totally positive Galois cohomology." Communications in Algebra, April 25, 2022, 1–22. http://dx.doi.org/10.1080/00927872.2022.2060995.

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50

Fernández, Víctor E., Natalie Paquette, and Brian Williams. "Twisted holography on AdS$_3 \times S^3 \times$ K3 & the planar chiral algebra." SciPost Physics 17, no. 4 (2024). http://dx.doi.org/10.21468/scipostphys.17.4.109.

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In this work, we revisit and elaborate on twisted holography for AdS_3 × S^3 × X3×S3×X with X= T^4X=T4, K3, with a particular focus on K3. We describe the twist of supergravity, identify the corresponding (generalization of) BCOV theory, and enumerate twisted supergravity states. We use this knowledge, and the technique of Koszul duality, to obtain the N → ∞N→∞, or planar, limit of the chiral algebra of the dual CFT. The resulting symmetries are strong enough to fix planar 2 and 3-point functions in the twisted theory or, equivalently, in a 1/4-BPS subsector of the original duality. This techn

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