Related papers: Piecewise hereditary algebras under field extensio…

Let $t$ be a positive integer and $\mathcal{A}$ a hereditary abelian category satisfying some finiteness conditions. We define the semi-derived Ringel-Hall algebra of $\mathcal{A}$ from the category $\mathcal{C}_{\mathbb{Z}/t}(\mathcal{A})$…

A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and…

We try to classify Hopf algebras with the Chevalley property according to their derived representation type. We show that a finite-dimensional indecomposable non-semisimple Hopf algebra $H$ with the Chevalley property is derived discrete if…

Let $\mathcal {A}$ be a finitary hereditary abelian category. We define a Hall algebra for the root category of $\mathcal {A}$ by applying the derived Hall numbers of the bounded derived category $D^b(\mathcal {A})$, which is proved to be…

Let $p$ and $q$ be two positive primes. Let $\ell$ be an odd positive prime integer and $F$ a quadratic number field. Let $K$ be an extension of $F$ such that $K$ is a dihedral extension of $\Q$ of degree $\ell$ over $F$ or $K$ is an…

An extension $K/k$ of analytic (i.e. real valued complete) fields is called small if it is topologically-algebraically generated by finitely many elements. We prove that this property is inherited by subextensions and hence topological…

We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two…

We show that if a (not necessarily algebraic) triangulated category T contains an admissible hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful triangle functor from the whole of the bounded…

We call a finite dimensional algebra A S-connected if the projective dimensions of the simple A-modules form an interval. We prove that a Nakayama algebra A is S-connected if and only if A is quasi-hereditary. We apply this result to…

Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$…

In this paper we describe several characterizations of basic finite-dimensional $k$-algebras $A$ stratified for all linear orders, and classify their graded algebras as tensor algebras satisfying some extra property. We also discuss whether…

We classify $n$-hereditary monomial algebras in three natural contexts: First, we give a classification of the $n$-hereditary truncated path algebras. We show that they are exactly the $n$-representation-finite Nakayama algebras classified…

Let $(K, v)$ be a Henselian discrete valued field with a quasifinite residue field. This paper proves the existence of an algebraic extension $E/K$ satisfying the following: (i) $E$ has dimension dim$(E) \le 1$, i.e. the Brauer group Br$(E…

Let F be a field of characteristic p. We define and investigate nonassociative differential extensions of F and of a central simple division algebra over F and give a criterium for these algebras to be division. As special cases, we obtain…

In this paper we answer two questions from [16], by showing that, over any algebraically closed field, $K$, there is a finitely generated, infinitely dimensional algebra $A$ such that algebras $A\otimes_{K}A$ and $A\otimes_{K} A^{op}$ are…

Let $B\subset A$ be a left or right bounded extension of finite dimensional algebras. We use the Jacobi-Zariski long nearly exact sequence to show that $B$ satisfies Han's conjecture if and only if $A$ does, regardless if the extension…

We prove that $\delta$-derivations of a simple finite-dimensional Lie algebra over a field of characteristic zero, with values in a finite-dimensional module, are either inner derivations, or, in the case of adjoint module, multiplications…

Let $Q$ be a finite quiver without loops. Then there is an admissible ideal $I$ such that the algebra $kQ/I$ has global dimension at most two and is (strongly) quasi-hereditary. In addition some other (strongly) quasi-hereditary algebras…

This article concerns commutative algebras over a field $k$ of characteristic zero which are finite dimensional as vectorspaces, and particularly those of such algebras which are graded. Here the term graded is applied to non-negatively…

In this paper we give an explicit algorithm to construct the ordinary quiver of a finite EI category for which the endomorphism groups of all objects have orders invertible in the field k. We classify all finite EI categories with…