The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra

Edward L. Green; Nicole Snashall

Displaying similar documents to “The Hochschild cohomology ring modulo nilpotence of a stacked monomial algebra”

Algebras of the cohomology operations in some cohomology theories

A. Jankowski

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Contents0. Introduction............................................................................................................................................. 51. Preliminaries.......................................................................................................................................... 62. Generalized cohomology theories with a coefficient group $Z_{p}$ .............................................. 83. Cohomology theory BP* ( , $Z_{p}$ )........................................................................................................

Standardly stratified split and lower triangular algebras

Eduardo do N. Marcos, Hector A. Merklen, Corina Sáenz (2002)

Colloquium Mathematicae

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In the first part, we study algebras A such that A = R ⨿ I, where R is a subalgebra and I a two-sided nilpotent ideal. Under certain conditions on I, we show that A is standardly stratified if and only if R is standardly stratified. Next, for $A = [\begin{matrix} U & 0 \\ M & V \end{matrix}]$ , we show that A is standardly stratified if and only if the algebra R = U × V is standardly stratified and $_{V} M$ is a good V-module.

Motivic cohomology and unramified cohomology of quadrics

Bruno Kahn, R. Sujatha (2000)

Journal of the European Mathematical Society

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This is the last of a series of three papers where we compute the unramified cohomology of quadrics in degree up to 4. Complete results were obtained in the two previous papers for quadrics of dimension $\leq 4$ and $\geq 11$ . Here we deal with the remaining dimensions between 5 and 10. We also prove that the unramified cohomology of Pfister quadrics with divisible coefficients always comes from the ground field, and that the same holds for their unramified Witt rings. We apply these results to real...

Leibniz $A$ -algebras

David A. Towers (2020)

Communications in Mathematics

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A finite-dimensional Lie algebra is called an $A$ -algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of describing residually finite varieties. They have been studied by several authors, including Bakhturin, Dallmer, Drensky, Sheina, Premet, Semenov, Towers and Varea. In this paper we establish generalisations of many of these results to Leibniz algebras. ...

A review of Lie superalgebra cohomology for pseudoforms

Carlo Alberto Cremonini (2022)

Archivum Mathematicum

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This note is based on a short talk presented at the “42nd Winter School Geometry and Physics” held in Srni, Czech Republic, January 15th–22nd 2022. We review the notion of Lie superalgebra cohomology and extend it to different form complexes, typical of the superalgebraic setting. In particular, we introduce pseudoforms as infinite-dimensional modules related to sub-superalgebras. We then show how to extend the Koszul-Hochschild-Serre spectral sequence for pseudoforms as a computational...

Hochschild (co)homology of Yoneda algebras of reconstruction algebras of type $𝐀_{1}$

Bo Hou, Yanhong Guo (2015)

Czechoslovak Mathematical Journal

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The reconstruction algebra is a generalization of the preprojective algebra, and plays important roles in algebraic geometry and commutative algebra. We consider the homological property of this class of algebras by calculating the Hochschild homology and Hochschild cohomology. Let $Λ_{t}$ be the Yoneda algebra of a reconstruction algebra of type $𝐀_{1}$ over a field $. I n t h i s p a p e r, a m i n i m a l p r o j e c t i v e b i m o d u l e r e s o l u t i o n o f$ t $i s c o n s t r u c t e d, a n d t h e$ -dimensions of all Hochschild homology and cohomology groups of $Λ_{t}$ are calculated explicitly.

Overconvergent de Rham-Witt cohomology

Christopher Davis, Andreas Langer, Thomas Zink (2011)

Annales scientifiques de l'École Normale Supérieure

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The goal of this work is to construct, for a smooth variety $X$ over a perfect field k of finite characteristic $p > 0$ , an overconvergent de Rham-Witt complex $W^{†} Ω_{X / k}$ as a suitable subcomplex of the de Rham-Witt complex of Deligne-Illusie. This complex, which is functorial in $X$ , is a complex of étale sheaves and a differential graded algebra over the ring $W^{†} (𝒪_{X})$ of overconvergent Witt-vectors. If $X$ is affine one proves that there is an isomorphism between Monsky-Washnitzer cohomology and (rational) overconvergent...

$L^{2}$ -cohomology

J. Eichhorn (1986)

Banach Center Publications

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A property for locally convex *-algebras related to property (T) and character amenability

Xiao Chen, Anthony To-Ming Lau, Chi-Keung Ng (2015)

Studia Mathematica

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For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let $C_{c} (G)$ be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that $(C_{c} (G), ε_{G})$ has property (FH) if and only if G has property...

Symmetries in connected graded algebras and their PBW-deformations

Yongjun Xu, Xin Zhang (2023)

Czechoslovak Mathematical Journal

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We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo’s quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a $𝒦_{2}$ algebra $𝒜$ which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra ${ℱ𝒦}_{3}$ , and explicitly construct all the (self-)symmetric and sign-(self-)symmetric...

Local-global principle for annihilation of general local cohomology

J. Asadollahi, K. Khashyarmanesh, Sh. Salarian (2001)

Colloquium Mathematicae

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Let A be a Noetherian ring, let M be a finitely generated A-module and let Φ be a system of ideals of A. We prove that, for any ideal in Φ, if, for every prime ideal of A, there exists an integer k(), depending on , such that $^{k ()}$ kills the general local cohomology module $H_{Φ_{}}^{j} (M_{})$ for every integer j less than a fixed integer n, where $Φ_{} : =_{} : \in Φ$ , then there exists an integer k such that $^{k} H_{Φ}^{j} (M) = 0$ for every j < n.

Quintasymptotic primes, local cohomology and ideal topologies

A. A. Mehrvarz, R. Naghipour, M. Sedghi (2006)

Colloquium Mathematicae

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Let Φ be a system of ideals on a commutative Noetherian ring R, and let S be a multiplicatively closed subset of R. The first result shows that the topologies defined by ${I_{a}}_{I \in Φ}$ and ${S (I_{a})}_{I \in Φ}$ are equivalent if and only if S is disjoint from the quintasymptotic primes of Φ. Also, by using the generalized Lichtenbaum-Hartshorne vanishing theorem we show that, if (R,) is a d-dimensional local quasi-unmixed ring, then $H_{Φ}^{d} (R)$ , the dth local cohomology module of R with respect to Φ, vanishes if and only if there...

On a Construction of ModularGMS-algebras

Abd El-Mohsen Badawy (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety ${\underset{̲}{𝐊}}_{2}$ by means of ${\underset{̲}{K}}_{2}$ -quadruples. We also characterize isomorphisms of these algebras by means of ${\underset{̲}{K}}_{2}$ -quadruples.

Engel BCI-algebras: an application of left and right commutators

Ardavan Najafi, Arsham Borumand Saeid (2021)

Mathematica Bohemica

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We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$ -Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular, we prove that any nilpotent BCI-algebra of type $2$ is an Engel BCI-algebra, but solvable BCI-algebras are not Engel, generally. Also, it is...

Division algebras that generalize Dickson semifields

Daniel Thompson (2020)

Communications in Mathematics

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We generalize Knuth’s construction of Case I semifields quadratic over a weak nucleus, also known as generalized Dickson semifields, by doubling of central simple algebras. We thus obtain division algebras of dimension $2 s^{2}$ by doubling central division algebras of degree $s$ . Results on isomorphisms and automorphisms of these algebras are obtained in certain cases.

The Wells map for abelian extensions of 3-Lie algebras

Youjun Tan, Senrong Xu (2019)

Czechoslovak Mathematical Journal

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The Wells map relates automorphisms with cohomology in the setting of extensions of groups and Lie algebras. We construct the Wells map for some abelian extensions $0 \to A ↪ L \overset{π}{\to} B \to 0$ of 3-Lie algebras to obtain obstruction classes in $H^{1} (B, A)$ for a pair of automorphisms in $Aut (A) \times Aut (B)$ to be inducible from an automorphism of $L$ . Application to free nilpotent 3-Lie algebras is discussed.