Universally Koszul and initially Koszul properties of Orlik–Solomon algebras

2019 ◽  
Vol 19 (11) ◽  
pp. 2050218
Author(s):  
Phong Dinh Thieu
Keyword(s):  
London Math ◽  
Exterior Algebra ◽  
Hyperplane Arrangements ◽  
Koszul Algebras ◽  
Graded Algebra ◽  
Standing Question

Let [Formula: see text] be a field with [Formula: see text] and [Formula: see text] an exterior algebra over [Formula: see text] with a standard grading [Formula: see text]. Let [Formula: see text] be a graded algebra, where [Formula: see text] is a graded ideal in [Formula: see text]. In this paper, we study universally Koszul and initially Koszul properties of [Formula: see text] and find classes of ideals [Formula: see text] which characterize such properties of [Formula: see text]. As applications, we classify arrangements whose Orlik–Solomon algebras are universally Koszul or initially Koszul. These results are related to a long-standing question of Shelton–Yuzvinsky [B. Shelton and S. Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc. 56 (1997) 477–490].

scholarly journals Multilinear Algebras and Tensors with Vector Subbundle of Manifolds

2015 ◽  
Vol 62 (1) ◽  
pp. 31-35
Author(s):  
Khondokar M Ahmed ◽  
Saraban Tahora
Keyword(s):  
Tensor Product ◽  
Exterior Algebra ◽  
Symmetric Algebra ◽  
Tensor Algebra ◽  
Graded Algebra ◽  
Algebra Module

In the present paper some aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundle are studied. A Theorem 1.32. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21957 Dhaka Univ. J. Sci. 62(1): 31-35, 2014 (January)

scholarly journals GRADED MORITA EQUIVALENCES FOR GEOMETRIC AS-REGULAR ALGEBRAS

2012 ◽  
Vol 55 (2) ◽  
pp. 241-257 ◽  
Author(s):  
IZURU MORI ◽  
KENTA UEYAMA
Keyword(s):  
Algebraic Geometry ◽  
Three Dimensional ◽  
Koszul Algebras ◽  
Graded Algebra ◽  
Graded Algebras ◽  
Regular Algebra ◽  
Morita Equivalent ◽  
Regular Algebras

AbstractClassification of AS-regular algebras is one of the major projects in non-commutative algebraic geometry. In this paper, we will study when given AS-regular algebras are graded Morita equivalent. In particular, for every geometric AS-regular algebra A, we define another graded algebra A, and show that if two geometric AS-regular algebras A and A' are graded Morita equivalent, then A and A' are isomorphic as graded algebras. We also show that the converse holds in many three-dimensional cases. As applications, we apply our results to Frobenius Koszul algebras and Beilinson algebras.

Koszul Algebras from Graphs and Hyperplane Arrangements

1997 ◽  
Vol 56 (3) ◽  
pp. 477-490 ◽  
Author(s):  
Brad Shelton ◽  
Sergey Yuzvinsky
Keyword(s):  
Hyperplane Arrangements ◽  
Koszul Algebras

Pablo Neruda's Transnational Modernist Networks: Colombo-Madrid-London-Buenos Aires (1927–1933)

2017 ◽  
Vol 12 (2) ◽  
pp. 198-225
Author(s):  
Patricia Novillo-Corvalán
Keyword(s):  
Chamber Music ◽  
Latin American ◽  
Buenos Aires ◽  
Cultural Institutions ◽  
Complex Composition ◽  
British Colonial ◽  
The One ◽  
Composition Process ◽  
In Transit ◽  
Standing Question

This article positions Pablo Neruda's poetry collection Residence on Earth I (written between 1925–1931 and published in 1933) as a ‘text in transit’ that allows us to trace the development of transnational modernist networks through the text's protracted physical journey from British colonial Ceylon (now Sri Lanka) to Madrid, and from José Ortega y Gasset's Revista de Occidente (The Western Review) to T. S. Eliot's The Criterion. By mapping the text's diasporic movement, I seek to reinterpret its complex composition process as part of an anti-imperialist commitment that proposes a form of aesthetic solidarity with artistic modernism in Ceylon, on the one hand, and as a vehicle through which to interrogate the reception and categorisation of Latin American writers and their cultural institutions in a British periodical such as The Criterion, on the other. I conclude with an examination of Neruda's idiosyncratic Spanish translation of Joyce's Chamber Music, which was published in the Buenos Aires little magazine Poesía in 1933, positing that this translation exercise takes to further lengths his decolonising views by giving new momentum to the long-standing question of Hiberno-Latin American relations.

Short Generating Functions for some Semigroup Algebras

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham
Keyword(s):  
Rational Function ◽  
Generating Functions ◽  
Hilbert Series ◽  
Simple Expression ◽  
Arbitrary Field ◽  
Graded Algebra ◽  
Semigroup Algebras ◽  
Positive Integers

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.

scholarly journals A symmetric Bloch–Okounkov theorem

2021 ◽  
Vol 8 (2) ◽  
Author(s):  
Jan-Willem M. van Ittersum
Keyword(s):  
Symmetric Functions ◽  
Graded Algebra ◽  
Symmetric Polynomials ◽  
Generating Series

AbstractThe algebra of so-called shifted symmetric functions on partitions has the property that for all elements a certain generating series, called the q-bracket, is a quasimodular form. More generally, if a graded algebra A of functions on partitions has the property that the q-bracket of every element is a quasimodular form of the same weight, we call A a quasimodular algebra. We introduce a new quasimodular algebra $$\mathcal {T}$$ T consisting of symmetric polynomials in the part sizes and multiplicities.

scholarly journals On polytopes and generalizations of the KLT relations

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nikhil Kalyanapuram
Keyword(s):  
Scattering Amplitudes ◽  
Large Class ◽  
Moduli Space ◽  
Differential Forms ◽  
Natural Generalization ◽  
Intersection Theory ◽  
Hyperplane Arrangements ◽  
Number Of Solutions ◽  
Scalar Theories ◽  
Double Copy

Abstract We combine the technology of the theory of polytopes and twisted intersection theory to derive a large class of double copy relations that generalize the classical relations due to Kawai, Lewellen and Tye (KLT). To do this, we first study a generalization of the scattering equations of Cachazo, He and Yuan. While the scattering equations were defined on ℳ0, n — the moduli space of marked Riemann spheres — the new scattering equations are defined on polytopes known as accordiohedra, realized as hyperplane arrangements. These polytopes encode as patterns of intersection the scattering amplitudes of generic scalar theories. The twisted period relations of such intersection numbers provide a vast generalization of the KLT relations. Differential forms dual to the bounded chambers of the hyperplane arrangements furnish a natural generalization of the Bern-Carrasco-Johansson (BCJ) basis, the number of which can be determined by counting the number of solutions of the generalized scattering equations. In this work the focus is on a generalization of the BCJ expansion to generic scalar theories, although we use the labels KLT and BCJ interchangeably.

Sign in / Sign up

Export Citation Format

Share Document