Damiano, Alberto Struppa, Daniele Vajiac, Adrian Vajiac, Mihaela
Published in
Journal of Geometric Analysis

We introduce the notion of antisyzygies, which studies the inverse problem of finding a system of PDEs, given compatibility conditions. The system obtained possesses the property of removability of compact singularities. We write explicit computations in the cases of the Cauchy-Fueter system and Maxwell’s system for electromagnetism, and we conclud...

Kämpf, Gesa Römer, Tim
Published in
manuscripta mathematica

The Orlik–Solomon algebra of a matroid can be considered as a quotient ring over the exterior algebra E. At first, we study homological properties of E-modules as e.g., complexity, depth and regularity. In particular, we consider modules with linear injective resolutions. We apply our results to Orlik–Solomon algebras of matroids and give formulas ...

Lü, Jia Feng
Published in
Acta Mathematica Sinica, English Series

The so-called weakly d-Koszul-type module is introduced and it turns out that each weakly d-Koszul-type module contains a d-Koszul-type submodule. It is proved that, M ∈ ℐd(A) if and only if M admits a filtration of submodules: 0 ⊂ U0 ⊂ U1 ⊂ ... ⊂ Up = M such that all Ui/Ui−1 are d-Koszul-type modules, from which we obtain that the finitistic dimen...

He, JiWei Wu, QuanShui
Published in
Science in China Series A: Mathematics

The concept of Koszulity for differential graded (DG, for short) modules is introduced. It is shown that any bounded below DG module with bounded Ext-group to the trivial module over a Koszul DG algebra has a Koszul DG submodule (up to a shift and truncation), moreover such a DG module can be approximated by Koszul DG modules (Theorem 3.6). Let A b...

Happel, Dieter Seidel, Uwe
Published in
Algebras and Representation Theory

Let k be an algebraically closed field. Let Λ be the path algebra over k of the linearly oriented quiver \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb A_n$\end...

Si, JunRu
Published in
Science in China Series A: Mathematics

The paper focuses on the 1-generated positively graded algebras with non-pure resolutions and mainly discusses a new kind of algebras called (s, t, d)-bi-Koszul algebras as the generalization of bi-Koszul algebras. An (s, t, d)-bi-Koszul algebra can be obtained from two periodic algebras with pure resolutions. The generation of the Koszul dual of a...

He, Jiwei Wu, Quanshui
Published in
Chinese Annals of Mathematics, Series B

The concept of Koszul differential graded (DG for short) algebra is introduced in [8]. Let A be a Koszul DG algebra. If the Ext-algebra of A is finite-dimensional, i.e., the trivial module Ak is a compact object in the derived category of DG A-modules, then it is shown in [8] that A has many nice properties. However, if the Ext-algebra is infinite-...

Bahri, A. Bendersky, M. Cohen, F.R. Gitler, S.
Published in
Advances in Mathematics

This article gives a natural decomposition of the suspension of generalized moment-angle complexes or partial product spaces which arise as polyhedral product functors described below. The geometrical decomposition presented here provides structure for the stable homotopy type of these spaces including spaces appearing in work of Goresky–MacPherson...

Xia, Qi
Published in
Applied Mathematics-A Journal of Chinese Universities

In this paper, we generalize two kinds of graded algebras, δ-Koszul algebras and Kp algebras, to the non-graded cases. The trivial modules of δ-Koszul algebras have pure resolutions, while those of Kp algebras admit non-pure resolutions. We provide necessary and sufficient conditions for a notherian semiperfect algebra either to be a quasi-δ-Koszul...

Zhang, Xiao Jin Huang, Zhao Yong
Published in
Acta Mathematica Sinica, English Series

Let Λ be an Artinian algebra and F an additive subbifunctor of ExtΛ1(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod Λ and S a cotilting module over Γ = End(T). Then Hom(−, T) induces a duality between F-al...