Results 1 to 10 of about 347 (81)
G-quadratic, LG-quadratic, and Koszul quotients of exterior algebras [PDF]
Communications in Algebra, 2022 This paper introduces the study of LG-quadratic quotients of exterior algebras, showing that they are Koszul, as in the commutative case. We construct an example of an LG-quadratic algebra that is not G-quadratic and another example that is Koszul but not LG-quadratic.
McCullough, Jason, Mere, Zachary
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Koszul algebras and quadratic duals in Galois cohomology [PDF]
Advances in Mathematics, 2021 We investigate the Galois cohomology of finitely generated maximal pro-$p$ quotients of absolute Galois groups. Assuming the well-known conjectural description of these groups, we show that Galois cohomology has the PBW property. Hence in particular it is a Koszul algebra. This answers positively a conjecture by Positselski in this case.
Quadrelli, C +3 more
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Drinfeld twists of Koszul algebras [PDF]
Communications in Algebra, 2023 Given a Hopf algebra H and a counital 2-cocycle μ on H, Drinfeld introduced a notion of twist which deforms an H-module algebra A into a new algebra Aμ. We show that when A is a quadratic algebra, and H acts on A by degree-preserving endomorphisms, then ...
Edward Jones-Healey
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The Structure of Koszul Algebras Defined by Four Quadrics [PDF]
Journal of Algebra, 2021 Avramov, Conca, and Iyengar ask whether β i (R) ≤ ( g i ) for all i when R = S/I is a Koszul algebra minimally defined by g quadrics. In recent work, we give an affirmative answer to this question when g ≤ 4 by completely classifying the possible Betti ...
P. Mantero, Matthew Mastroeni
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Infinite-Dimensional Lie Bialgebras via Affinization of Novikov Bialgebras and Koszul Duality [PDF]
Communications in Mathematical Physics, 2023 Balinsky and Novikov showed that the affinization of a Novikov algebra naturally defines a Lie algebra, a property that in fact characterizes the Novikov algebra. It is also an instance of the operadic Koszul duality.
Yanyong Hong, C. Bai, Li Guo
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Higher preprojective algebras, Koszul algebras, and superpotentials [PDF]
Compositio Mathematica, 2019 In this article we study higher preprojective algebras, showing that various known results for ordinary preprojective algebras generalize to the higher setting.
Joseph Grant, O. Iyama
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Koszul Gorenstein algebras from Cohen-Macaulay simplicial complexes [PDF]
, 2021 We associate with every pure flag simplicial complex $\Delta$ a standard graded Gorenstein $\mathbb{F}$-algebra $R_{\Delta}$ whose homological features are largely dictated by the combinatorics and topology of $\Delta$.
Alessio D'Alì, Lorenzo Venturello
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Resolutions of operads via Koszul (bi)algebras
Journal of Homotopy and Related Structures, 2022 We introduce a construction that produces from each bialgebra H an operad AssH\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}
Pedro Tamaroff
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Poincar\'e duality for Koszul algebras [PDF]
, 2012 We discuss the consequences of the Poincar\'e duality, versus AS- Gorenstein property, for Koszul algebras (homogeneous and non homogeneous). For homogeneous Koszul algebras, the Poincar\'e duality property implies the existence of twisted potentials ...
M. Dubois-Violette
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Noncommutative Koszul algebras from combinatorial topology [PDF]
, 2008 Associated to any uniform finite layered graph Γ there is a noncommutative graded quadratic algebra A(Γ) given by a construction due to Gelfand, Retakh, Serconek and Wilson. It is natural to ask when these algebras are Koszul. Unfortunately, a mistake in
T. Cassidy, C. Phan, B. Shelton
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