Related papers: Self-injective algebras with hereditary stable sli…

Let $L$ denote a finite lattice with at least two points and let $A$ denote the incidence algebra of $L$. We prove that $L$ is distributive if and only if $A$ is an Auslander regular ring, which gives a homological characterisation of…

This paper deals with stratifying systems over hereditary algebras. In the case of tame hereditary algebras we obtain a bound for the size of the stratifying systems composed only by regular modules and we conclude that stratifying systems…

We provide sufficient conditions for a component of the Auslander-Reiten quiver of an artin algebra to be determined by the composition factors of its indecomposable modules.

We analyze Auslander-Reiten quivers of functorially finite resolving subcategories. Chapter 1 gives a short introduction into the basic definitions and theorems of Auslander-Reiten theory in A-mod. We generalize these definitions and…

Building on work of Gerstenhaber, we show that the space of integrable derivations on an Artin algebra $A$ forms a Lie algebra, and a restricted Lie algebra if $A$ contains a field of characteristic $p$. We deduce that the space of…

We show that Auslander algebras have a unique tilting and cotilting module which is generated and cogenerated by a projective-injective; its endomorphism ring is called the projective quotient algebra. For any representation-finite algebra,…

We develop a structure theory for two classes of infinite dimensional modules over tame hereditary algebras: the Baer modules, and the Mittag-Leffler ones.

Motivated by the structure of the algebras associated to the blocks of the BGG-category O we define a subclass of quasi-hereditary algebras called 1-quasi-hereditary. Many properties of these algebras only depend on the defining partial…

We give a complete description of all special biserial cluster-tilted algebras over a finite dimensional hereditary algebra H over an algebraically closed field K.

Let A be a finite-dimensional, self-injective algebra, graded in non-positive degree. We define A-dgstab, the differential graded stable category of A, to be the quotient of the bounded derived category of dg-modules by the thick…

Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…

In this article we obtain lower and upper bounds for global dimensions of a class of artinian algebras in terms of global dimensions of a finite subset of their artinian subalgebras. Finding these bounds for the global dimension of an…

We provide a unified approach, via deformations of incidence algebras, to several important types of representations with finiteness conditions, as well as the combinatorial algebras which produce them. We show that over finite dimensional…

In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.

In this paper we study injective modules over universal enveloping algebras of finite-dimensional Lie algebras over fields of arbitrary characteristic. Most of our results are dealing with fields of prime characteristic but we also…

Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…

We determined the $\tau$-tilting finiteness of Schur algebras over an algebraically closed field of arbitrary characteristic, except for a few small cases.

Let $A$ be a finite dimensional algebra over an algebraically closed field $\mathbf{k}$. If $A$ is quasi-hereditary and the projective dimensions of all standard modules are at most one, then $A$ is called left strongly quasi-hereditary. In…

The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central division F-algebra having the same maximal subfields as D. For…

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.