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Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

Jian Qiu, Maxim Zabzine (2011)

Archivum Mathematicum

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV–formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present...

Koszul and quasi-Koszul algebras obtained by tilting

R. M. Aquino, E. L. Green, E. N. Marcos (2002)

Colloquium Mathematicae

Given a finite-dimensional algebra, we present sufficient conditions on the projective presentation of the algebra modulo its radical for a tilted algebra to be a Koszul algebra and for the endomorphism ring of a tilting module to be a quasi-Koszul algebra. One condition we impose is that the algebra has global dimension no greater than 2. One of the main techniques is studying maps between the direct summands of the tilting module. Some applications are given. We also show that a Brenner-Butler...

Koszul duality for N-Koszul algebras

Roberto Martínez-Villa, Manuel Saorín (2005)

Colloquium Mathematicae

The correspondence between the category of modules over a graded algebra and the category of graded modules over its Yoneda algebra was studied in [8] by means of A ∞ algebras; this relation is very well understood for Koszul algebras (see for example [5],[6]). It is of interest to look for cases such that there exists a duality generalizing the Koszul situation. In this paper we will study N-Koszul algebras [1], [7], [9] for which such a duality exists.

Laura algebras and quasi-directed components

Marcelo Lanzilotta, David Smith (2006)

Colloquium Mathematicae

Using a notion of distance between indecomposable modules we deduce new characterizations of laura algebras and quasi-directed Auslander-Reiten components. Afterwards, we investigate the infinite radical of Artin algebras and show that there exist infinitely many non-directing modules between two indecomposable modules X and Y if r a d A ∞ ( X , Y ) ≠ 0 . We draw as inference that a convex component is quasi-directed if and only if it is almost directed.

Left EM rings

Jongwook Baeck (2024)

Czechoslovak Mathematical Journal

Let R [ x ] be the polynomial ring over a ring R with unity. A polynomial f ( x ) ∈ R [ x ] is referred to as a left annihilating content polynomial (left ACP) if there exist an element r ∈ R and a polynomial g ( x ) ∈ R [ x ] such that f ( x ) = r g ( x ) and g ( x ) is not a right zero-divisor polynomial in R [ x ] . A ring R is referred to as left EM if each polynomial f ( x ) ∈ R [ x ] is a left ACP. We observe the structure of left EM rings with various properties, and study the relationships between the one-sided EM condition and other standard ring theoretic conditions. Moreover,...

Left sections and the left part of an artin algebra

Ibrahim Assem (2009)

Colloquium Mathematicae

We define a notion of left section in an Auslander-Reiten component, by weakening one of the axioms for sections. We derive a generalisation of the Liu-Skowroński criterion for tilted algebras, then apply our results to describe the Auslander-Reiten components lying in the left part of an artin algebra.

Left-sided quasi-invertible bimodules over Nakayama algebras

Zygmunt Pogorzały (2005)

Open Mathematics

Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence.

Les ( a , b ) -algèbres à homotopie près

Walid Aloulou (2010)

Annales mathématiques Blaise Pascal

On étudie dans cet article les notions d’algèbre à homotopie près pour une structure définie par deux opérations . et [ , ] . Ayant déterminé la structure des G ∞ algèbres et des P ∞ algèbres, on généralise cette construction et on définit la stucture des ( a , b ) -algèbres à homotopie près. Etant donnée une structure d’algèbre commutative et de Lie différentielle graduée pour deux décalages des degrés donnés par a et b , on donnera une construction explicite de l’algèbre à homotopie près associée et on précisera...

Limits of tilting modules

Clezio A. Braga, Flávio U. Coelho (2009)

Colloquium Mathematicae

We study the problem of when a direct limit of tilting modules is still a tilting module.

Local cohomology in classical rings.

José Luis Bueso Montero, Pascual Jara Martínez (1992)

Publicacions Matemàtiques

The aim of this paper is to establish the close connection between prime ideals and torsion theories in a non necessarily commutative noetherian ring. We introduce a new definition of support of a module and characterize some kinds of torsion theories in terms of prime ideals. Using the machinery introduced before, we prove a version of the Mayer-Vietoris Theorem for local cohomology and establish a relationship between the classical dimension and the vanishing of the groups of local cohomology...

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