These lecture notes are about the variety Mod (A, r) of r-dimensional modules for an
associative algebra A, and to a lesser extent about the variety Alg (n) of n-dimensional …

In this paper we define (special) GLIT classes and (special) GLIT algebras. We prove that
GLIT algebras, which generalise Lat-Igusa-Todorov algebras, satisfy the finitistic dimension …

In this paper we study stable finiteness of ample groupoid algebras with applications to
inverse semigroup algebras and Leavitt path algebras, recovering old results and proving …

We introduce a new class of infinite-dimensional Lie algebras, which we refer to as
continuum Kac-Moody algebras. Their construction is closely related to that of usual Kac …

Representation theory is the study of algebraic structures such as groups and rings via their
actions on simpler algebraic structures such as vector spaces. In this survey chapter, which …

For any truncated path algebra Λ, we give a structural description of the modules in the
categories P^< ∞ (Λ-\rm mod) and P^< ∞ (Λ-\rm mod), consisting of the finitely generated …

Publisher Summary This chapter discusses the use of the language of quivers in
mathematics. Quivers arise in many areas of mathematics, including representation theory …

A free semigroupoid algebra is the wot-closure of the algebra generated by a TCK family of
a graph. We obtain a structure theory for these algebras analogous to that of free semigroup …

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

In math. AG/9904171 it was shown that the étale local structure of finite dimensional
representations for a formally smooth algebra is determined by (varying) local quiver …