Quasitilted Extensions of Algebras, II

Tilting Theory and Quasitilted Algebras

On Auslander–Reiten components for quasitilted algebras

An artin algebra A over a commutative artin ring R is called quasitilted if gl.dimA ≤ 2 and for each indecomposable finitely generated A-module M we have pdM ≤ 1 or idM ≤ 1. In [11] several characterizations of quasitilted algebras were proven. We investigate the structure and homological properties of connected components in the Auslander–Reiten quiver ΓA of a quasitilted algebra A. Let A be a...

Almost Regular Auslander-reiten Components and Quasitilted Algebras

The problem of giving a general description of the shapes of AuslanderReiten components of an artin algebra has been settled for semiregular components (see [4, 9, 14]). Recently, S. Li has considered this problem for components in which every possible path from an injective module to a projective module is sectional. The result says that such a component is embeddable in some ZZ∆ with ∆ a quiv...

Extensions of Topological Algebras

We prove that, in the class of commutative topological algebras with separately continuous multiplication, an element is permanently singular if and only if it is a topological divisor of zero. This extends the result given by R. Arens [1] for the Banach algebra case. We also give sufficient conditions for non-removability of ideals in commutative topological algebras with jointly continuous mu...

Counting Using Hall Algebras Ii. Extensions from Quivers

We count the Fq-rational points of GIT quotients of quiver representations with relations. We focus on two types of algebras – one is one-point extended from a quiver Q, and the other is the Dynkin A2 tensored with Q. For both, we obtain explicit formulas. We study when they are polynomial-count. We follow the similar line as in the first paper but algebraic manipulations in Hall algebra will b...