Cancellative dimer algebras on a torus have many nice algebraic and homological
properties. However, these nice properties disappear for dimer algebras on higher genus …

The only connected finite-dimensional algebras with finitely many isomorphism classes of
indecomposable bimodules are the quotients of the path algebras of uniformly oriented A n …

Let A be a finite-dimensional algebra over an algebraically closed field F. We consider the
socle soc (Z (A)) of its center Z (A), which is known to be an ideal of Z (A). The principal …

We introduce a new class of partial actions of free groups on totally disconnected compact
Hausdorff spaces, which we call convex subshifts. These serve as an abstract framework for …

This is nothing more than a finite directed graph. We allow loops and multiple edges. The
only difference is that instead of defining the edges as ordered pairs of vertices we define …

We construct an explicit projective bimodule resolution for the Leavitt path algebra of a row-
finite quiver. We prove that the Leavitt path algebra of a row-countable quiver has …

Leavitt path algebras are a new and exciting subject in noncommutative ring theory. To each
directed graph E, and unital commutative ring R, is associated an R-algebra called the …

In this paper we focus on a certain self-distributive multiplication on coalgebras, which leads
to so-called rack bialgebra. Inspired by semi-group theory (adapting the Suschkewitsch …

A group graded $ K $-algebra $ A=\bigoplus\limits_ {g\in G} A_g $ is called" locally finite" if
$\dim_K A_g<\infty $ for every $ g\in G $. We characterise the weighted graphs $(E, w) $ for …

arXiv:math/0505082v1 [math.RA] 5 May 2005 Page 1 arXiv:math/0505082v1 [math.RA] 5 May
2005 FINITE-DIMENSIONAL ALGEBRAS AND QUIVERS ALISTAIR SAVAGE Abstract. This is …