Related papers: Wild Algebras: Two Examples

A conjectural generalization of the McKay correspondence in terms of stringy invariants to arbitrary characteristic, including the wild case, was recently formulated by the author in the case where the given finite group linearly acts on an…

In this paper we discuss, in terms of quivers with relations, sufficient and necessary conditions for an algebra to be a quasitilted algebra. We start with an algebra with global dimension two and we give a sufficient condition for it to be…

An example of a non-triangulable locally nilpotent derivation and an example of a wild exponential automorphism of the free Novikov algebra $N\left\langle x,y,z\right\rangle$ in three variables $x,y,z$ over a field of characteristic zero…

Given an Artinian algebra $A$ over a field $k$, there are several combinatorial objects associated to $A$. They are the diagram $D_A$ as defined in [DK], the natural quiver $\Delta_A$ defined in \cite{Li} (cf. Section 2), and a generalized…

We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.

An associative division algebra D is said to be _affine_ over a central subfield k if D is finitely generated as a k-algebra. In 1956 Amitsur famously proved that, when k is uncountable, D cannot be k-affine unless D is algebraic over k. In…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

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…

This paper deals with $n$-dimensional algebras, over any field, which have only trivial derivation (automorphism) and simple algebras. It is shown that the corresponding sets of algebras are not empty and, in algebraically closed field…

A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…

Let k be a perfect field and A a finite dimensional k-algebra of finite global dimension (e.g. the path algebra of a finite quiver without oriented cycles). Making use of the recent theory of noncommutative motives, we prove that the value…

There exists two types of nonassociative algebras whose associator satisfies a symmetric relation associated with a 1-dimensional invariant vector space with respect to the natural action of the symmetric group on three elements. The first…

We apply the notion of hyperfinite families of modules to the wild path algebras of generalised Kronecker quivers $k\Theta(d)$. While the preprojective and postinjective component are hyperfinite, we show the existence of a family of…

A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…

Brief proofs of classical results of Lie on finite dimensional subalgebras of vector fields in two and three variables are outlined. The results for algebras of maximal rank for vector fields in $\mathbb{C}^N$ -- $N$ arbitrary -- are also…

The aim of the paper is to discuss the relations between the three kinds of objects named in the title. In a sense, this is a survey of such relations; however, some new directions are also considered. This relates, especially, to sections…

A double algebra is a linear space $V$ equipped with linear map $V\otimes V\to V\otimes V$. Additional conditions on this map lead to the notions of Lie and associative double algebras. We prove that simple finite-dimensional Lie double…

We present coalgebras of some classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3-order symmetric group. Amongst these algebras we find the well-known Vinberg algebras, the…

We show that if $k$ is a countable field, then there exists a finitely generated, infinite-dimensional, primitive algebraic $k$-algebra $A$ whose Gelfand-Kirillov dimension is at most six. In addition to this we construct a two-generated…

W-algebras of finite type are certain finitely generated associative algebras closely related to the universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete…