Related papers: Koszul homomorphisms and universal resolutions in …

Let $R$ be a noetherian ring and $M$ a finite $R$-module. With a linear form $\chi$ on $M$ one associates the Koszul complex $K(\chi)$. If $M$ is a free module, then the homology of $K(\chi)$ is well-understood, and in particular it is…

We give an explicit quadratic Grobner basis for generalized Chow rings of supersolvable built lattices, with the help of the operadic structure on geometric lattices introduced in a previous article. This shows that the generalized Chow…

The concept of Koszul differential graded algebra (Koszul DG algebra) is introduced. Koszul DG algebras exist extensively, and have nice properties similar to the classic Koszul algebras. A DG version of the Koszul duality is proved. When…

We examine functorial and homotopy properties of the exotic characteristic homomorphism in the category of Lie algebroids which was lastly obtained by the authors in [4]. This homomorphism depends on a triple (A,B,$\nabla$) where B…

Let $\g$ be a reductive Lie algebra and $V$ a $\g$-semisimple module. In this article, we study the category $\G$ of graded finite-dimensional representations of $\g \ltimes V$. We produce a large class of truncated subcategories, which are…

Each connected graded, graded-commutative algebra $A$ of finite type over a field $\Bbbk$ of characteristic zero defines a complex of finitely generated, graded modules over a symmetric algebra, whose homology graded modules are called the…

In a paper in 1962, Golod proved that the Betti sequence of the residue field of a local ring attains an upper bound given by Serre if and only if the homology algebra of the Koszul complex of the ring has trivial multiplications and…

For a flat commutative $k$-algebra $A$ such that the enveloping algebra $A\otimes_k A$ is noetherian, given a finitely generated bimodule $M$, we show that the adic completion of the Hochschild cohomology module $HH^n(A/k,M)$ is naturally…

Let $\lie g$ be a simple Lie algebra and let $\bs^{\lie g}$ be the locally finite part of the algebra of invariants $(_\bc\bv\otimes S(\lie g))^{\lie g}$ where $\bv$ is the direct sum of all simple finite-dimensional modules for $\lie g$…

Let I be an ideal of a Complete Cohen-Macaulay local ring R of dimension n. We wil show that the natural homomorphism Rto HomR(HcI(KR), HcI(KR)) is an isomorphism provided that I is a cohomologically compltete intersection ideal of grade c…

Given a simply connected space $X$, there are several, a priori different, algebraic groups whose groups of $\mathbb Q$-points are isomorphic to the group of homotopy classes of homotopy automorphisms of the rationalization of $X$. We will…

Suppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $\mathcal{E}$ with enough flat projectives, such as the category of complete bornological spaces $\textbf{CBorn}_k$ or the category of inductive limits of…

We prove a Cohen-Macaulay version of a result by Avramov-Golod and Frankild-J{\o}rgensen about Gorenstein rings, showing that if a noetherian ring $A$ is Cohen-Macaulay, and $a_1,\dots,a_n$ is any sequence of elements in $A$, then the…

We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When…

A residue-theoretic representation is given for massless matter fields in (quotients) of (weighted) \CY\ complete intersection models and the corresponding chiral operators in \LGO{s}. The well known polynomial deformations are thus…

Let $R$ be a standard graded Gorenstein algebra over a field presented by quadrics. Conca, Rossi, and Valla have shown that such a ring is Koszul if $\mathrm{reg}\, R \leq 2$ or if $\mathrm{reg}\, = 3$ and $c= \mathrm{codim}\, R \leq 4$,…

Let $I$ be an ideal of a commutative Noetherian ring $R$. Let $M$ and $N$ be any $R$-modules. We define the generalized completion homology modules $L_i\Lambda^I (N,M)$, for $i\in \mathbb{Z}$, as the homologies of the complex…

Working in the context of symmetric spectra, we consider any higher algebraic structures that can be described as algebras over an operad O. We prove that the fundamental adjunction comparing O-algebra spectra with coalgebra spectra over…

Several spectral sequence techniques are used in order to derive information about the structure of finite free resolutions of graded modules. These results cover estimates of the minimal number of generators of defining ideals of…

Hochster established the existence of a commutative noetherian ring $\Cal R$ and a universal resolution $\Bbb U$ of the form $0\to \Cal R^{e}\to \Cal R^{f}\to \Cal R^{g}\to 0$ such that for any commutative noetherian ring $S$ and any…