Related papers: Algebras with homogeneous module category are tame

Let $\Lambda$ be an Auslander's 1-Gorenstein Artinian algebra with global dimension two. If $\Lambda$ admits a trivial maximal 1-orthogonal subcategory of $\mod\Lambda$, then for any indecomposable module $M \in \mod \Lambda$, we have that…

We prove an abstract Birkhoff normal form theorem for Hamiltonian Partial Differential Equations. The theorem applies to semilinear equations with nonlinearity satisfying a property that we call of Tame Modulus. Such a property is related…

Let $A$ be a finite dimensional symmetric Hopf algebra over a field $k$. We show that there are $A$-modules whose Tate cohomology is not finitely generated over the Tate cohomology ring of $A$. However, we also construct $A$-modules which…

In this paper we study the behaviour of modules over finite dimensional algebras whose endomorphism algebra is a division ring. We show that there are finitely many such modules in the module category of an algebra if and only if the length…

Finite-dimensional Jacobian algebras are studied from the perspective of representation types. We establish that (like other representation types) the notions of $E$-finiteness and $E$-tameness are invariant under mutations of quivers with…

Homological algebra of modules over posets is developed, as closely parallel as possible to that of finitely generated modules over noetherian commutative rings, in the direction of finite presentations and resolutions. Centrally at issue…

In a recent paper it has been established that over an Artinian ring R all two-dimensional polynomial automorphisms having Jacobian determinant one are tame if R is a Q-algebra. This is a generalization of the famous Jung-Van der Kulk…

Let k be a field, let A a finite-dimensional hereditary k-algebra. We consider the category of all finite-dimensional A-modules. We are going to characterize the representation type of A (tame or wild) in terms of the possible subcategories…

Let $\Lambda$ be a finite dimensional Auslander algebra. For a $\Lambda$-module $M$, we prove that the projective dimension of $M$ is at most one if and only if the projective dimension of its socle soc\,$M$ is at most one. As an…

Let $\Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $\Gamma$ be the Auslander algebra of $\Lambda$. Then every indecomposable direct summand of a tilting $\Gamma$-module is either simple or projective.…

We prove that separable, simple, unital, non-elementary, stably finite C*-algebras that have stable rank one, and that have locally finite nuclear dimension in a tracial sense, have uniform property $\Gamma$. In particular, Villadsen…

The object of this paper is the tameness conjecture which describes an arbitrary graded k-algebra homomorphism of polytopal rings. We give further evidence of this conjecture by showing supporting results concerning joins, multiples and…

We prove that the uniformizing map of any arithmetic quotient, as well as the period map associated to any pure polarized $\mathbb{Z}$-variation of Hodge structure $\mathbb{V}$ on a smooth complex quasi-projective variety $S$, are…

We provide a complete classification of all tame and wild symmetric special multiserial algebras in terms of the underlying Brauer configuration. Our classification contains the symmetric special multiserial algebras of finite…

Consider tuples of separable algebras over a common local or global number field, related to each other by specified resolvent constructions. Under the assumption that all ramification is tame, simple group-theoretic calculations give best…

We study the dynamical properties of irregular model sets and show that the translation action on their hull always admits an infinite independence set. The dynamics can therefore not be tame and the topological sequence entropy is strictly…

A celebrated result in representation theory is that of higher Auslander correspondence. Let $\Lambda$ an Artin algebra and $X$ a $d$-cluster-tilting module. Iyama has shown that the endomorphism ring $\Gamma$ of $X$ is a $d$-Auslander…

For the algebra $I_n$ of polynomial integro-differential operators over a field $K$ of characteristic zero, a classification of simple weight and generalized weight (left and right) $I_n$-modules is given. It is proven that the category of…

The two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence.…

The numerical invariants (global) cohomological length, (global) cohomological width, and (global) cohomological range of complexes (algebras) are introduced. Cohomological range leads to the concepts of derived bounded algebras and…