Displaying similar documents to “Koszul duality for N-Koszul algebras”

Ext-algebras and derived equivalences

Dag Madsen (2006)

Colloquium Mathematicae

Similarity:

Using derived categories, we develop an alternative approach to defining Koszulness for positively graded algebras where the degree zero part is not necessarily semisimple.

Parametric representations of BiHom-Hopf algebras

Xiaohui Zhang, Wei Wang, Juzhen Chen (2024)

Czechoslovak Mathematical Journal

Similarity:

The main purpose of the present paper is to study representations of BiHom-Hopf algebras. We first introduce the notion of BiHom-Hopf algebras, and then discuss BiHom-type modules, Yetter-Dinfeld modules and Drinfeld doubles with parameters. We get some new n -monoidal categories via the category of BiHom-(co)modules and the category of BiHom-Yetter-Drinfeld modules. Finally, we obtain a center construction type theorem on BiHom-Hopf algebras.

Isomorphisms between graded Frobenius algebras constructed from twisted superpotentials

Xuejun Xia, Libin Li (2022)

Czechoslovak Mathematical Journal

Similarity:

In order to distinguish the connected graded Frobenius algebras determined by different twisted superpotentials, we introduce the nondegeneracy of twisted superpotentials. We give the sufficient and necessary condition for connected graded Frobenius algebras determined by two nondegenerate twisted superpotentials to be isomorphic. As an application, we classify the connected ℤ -graded Frobenius algebra of length 3, whose dimension of the degree 1 is 2.

On Auslander-Reiten translates in functorially finite subcategories and applications

K. Erdmann, D. Madsen, V. Miemietz (2010)

Colloquium Mathematicae

Similarity:

We consider functorially finite subcategories in module categories over Artin algebras. One main result provides a method, in the setup of bounded derived categories, to compute approximations and the end terms of relative Auslander-Reiten sequences. We also prove an Auslander-Reiten formula for the setting of functorially finite subcategories. Furthermore, we study the category of modules filtered by standard modules for certain quasi-hereditary algebras and we classify precisely when...

Hopf algebras and dendriform structures arising from parking functions

Jean-Christophe Novelli, Jean-Yves Thibon (2007)

Fundamenta Mathematicae

Similarity:

We introduce a graded Hopf algebra based on the set of parking functions (hence of dimension ( n + 1 ) n - 1 in degree n). This algebra can be embedded into a noncommutative polynomial algebra in infinitely many variables. We determine its structure, and show that it admits natural quotients and subalgebras whose graded components have dimensions respectively given by the Schröder numbers (plane trees), the Catalan numbers, and powers of 3. These smaller algebras are always bialgebras and belong to...

Laura algebras and quasi-directed components

Marcelo Lanzilotta, David Smith (2006)

Colloquium Mathematicae

Similarity:

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.

Deformed mesh algebras of Dynkin type ℂₙ

Jerzy Białkowski, Karin Erdmann, Andrzej Skowroński (2012)

Colloquium Mathematicae

Similarity:

In our recent paper (J. Algebra 345 (2011)) we prove that the deformed preprojective algebras of generalized Dynkin type ₙ (in the sense of our earlier work in Trans. Amer Math. Soc. 359 (2007)) are exactly (up to isomorphism) the stable Auslander algebras of simple plane singularities of Dynkin type 2 n . In this article we complete the picture by showing that the deformed mesh algebras of Dynkin type ℂₙ are isomorphic to the canonical mesh algebras of type ℂₙ, and hence to the stable...

Tilting slice modules over minimal 2-fundamental algebras

Zygmunt Pogorzały, Karolina Szmyt (2008)

Colloquium Mathematicae

Similarity:

A class of finite-dimensional algebras whose Auslander-Reiten quivers have starting but not generalized standard components is investigated. For these components the slices whose slice modules are tilting are considered. Moreover, the endomorphism algebras of tilting slice modules are characterized.

Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin (2010)

Banach Center Publications

Similarity:

A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of G ∞ -generalized functions class are given. A straightforward relationship between the classical and the generalized...

On restrictions of indecomposables of tame algebras

R. Bautista, E. Pérez, L. Salmerón (2011)

Colloquium Mathematicae

Similarity:

We continue the study of ditalgebras, an acronym for "differential tensor algebras", and of their categories of modules. We examine extension/restriction interactions between module categories over a ditalgebra and a proper subditalgebra. As an application, we prove a result on representations of finite-dimensional tame algebras Λ over an algebraically closed field, which gives information on the extension/restriction interaction between module categories of some special algebras Λ₀,...

On two tame algebras with super-decomposable pure-injective modules

Stanisław Kasjan, Grzegorz Pastuszak (2011)

Colloquium Mathematicae

Similarity:

Let k be a field of characteristic different from 2. We consider two important tame non-polynomial growth algebras: the incidence k-algebra of the garland 𝒢₃ of length 3 and the incidence k-algebra of the enlargement of the Nazarova-Zavadskij poset 𝒩 𝓩 by a greatest element. We show that if Λ is one of these algebras, then there exists a special family of pointed Λ-modules, called an independent pair of dense chains of pointed modules. Hence, by a result of Ziegler, Λ admits a super-decomposable...