Related papers: Homogeneity implies Tameness

The celebrated Drozd's theorem asserts that a finite-dimensional basic algebra $\Lambda$ over an algebraically closed field $k$ is either tame or wild, whereas the Crawley-Boevey's theorem states that given a tame algebra $\Lambda$ and a…

Let $\Lambda$ be a finite-dimensional algebra over an algebraically closed field, then $\Lambda$ is either tame or wild. Is there any homological description in terms of AR-translations on tameness? Or equivalently, is there any…

We prove the tame-wild dichotomy conjecture, due to D. Simson, for infinite dimensional algebras and coalgebras. The key part of the approach is proving new representation theoretic characterizations local finiteness. Among other, we show…

We show that a tilted algebra $A$ is tame if and only if for each generic root $\dd$ of $A$ and each indecomposable irreducible component $C$ of $\module(A,\dd)$, the field of rational invariants $k(C)^{\GL(\dd)}$ is isomorphic to $k$ or…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. The proof is based on the technique of matrix problems (boxes and reduction algorithm). It implies, in particular,…

We introduce the notion of interlaced weak ditalgebras and apply reduction procedures to their module categories to prove a tame-wild dichotomy for the category ${\cal F}(\Delta)$ of $\Delta$-filtered modules for an arbitrary finite…

Birge Huisgen-Zimmermann calls a finite dimensional algebra homologically tame provided the little and the big finitistic dimension are equal and finite. The question formulated in the title has been discussed by her in the paper…

We prove that every finite dimensional algebra over an algebraically closed field is either derived tame or derived wild. We also prove that any deformation of a derived tame algebra is derived tame.

Let $\mathbf{k}$ be a field of any characteristic and let $\Lambda$ be a finite dimensional $\mathbf{k}$-algebra. We prove that if $V$ is a finite dimensional right $\Lambda$-module that lies in the mouth of a stable homogeneous tube…

We show that a finite connected quiver Q with no oriented cycles is tame if and only if for each dimension vector $\mathbf{d}$ and each integral weight $\theta$ of Q, the moduli space $\mathcal{M}(Q,\mathbf{d})^{ss}_{\theta}$ of…

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…

Consider a finite-dimensional algebra $A$ and any of its moduli spaces $\mathcal{M}(A,\mathbf{d})^{ss}_{\theta}$ of representations. We prove a decomposition theorem which relates any irreducible component of…

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first…

Let $\Lambda$ be an Artin algebra. A GR segment of $\Lambda$ is a sequence of GR measures which is closed under direct successors and direct predecessors. The number of the GR segments was conjectured to relate to the representation type of…

We give a criterion of tameness and wildness for a finite-dimensional Lie algebra over an algebraically closed field.

It is shown that path algebras modulo relations of the form $\Lambda = KQ/I$, where $Q$ is a quiver, $K$ a coefficient field, and $I \subseteq KQ$ the ideal generated by all paths of a given length, can be readily analyzed homologically,…

All spaces are assumed to be separable and metrizable. We show that, assuming the Axiom of Determinacy, every zero-dimensional homogeneous space is strongly homogeneous (that is, all its non-empty clopen subspaces are homeomorphic), with…

We prove that the number of parameters defining a complex of projective modules over a finite dimensional algebra is upper semi-continuous in families of algebras. Supposing that every algebra is either derived tame or derived wild, we get…

We show that string algebras are `homologically tame' in the following sense: First, the syzygies of arbitrary representations of a finite dimensional string algebra $\Lambda$ are direct sums of cyclic representations, and the left…

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…