We study a new class of quiver algebras on surfaces, called'geodesic ghor algebras'. These
algebras generalize cancellative dimer algebras on a torus to higher genus surfaces, where …

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

A ghor algebra is the path algebra of a dimer quiver on a surface, modulo relations that
come from the perfect matchings of its quiver. Such algebras arise from abelian quiver …

Let A be a nondegenerate dimer (or ghor) algebra on a torus, and let Z be its center. Using
cyclic contractions, we show the following are equivalent: A is noetherian; Z is noetherian; A …

We define a new algebra associated to a Legendrian submanifold $\Lambda $ of a contact
manifold of the form $\mathbb {R} _ {t}\times W $, called the planar diagram algebra and …

In this paper, we study a preprojective algebra for quivers decorated with k-algebras and
bimodules, which generalizes work of Gabriel for ordinary quivers, work of Dlab and Ringel …

We provide a differential structure on arbitrary cleft extensions $ B:= A^{\mathrm {co}
H}\subseteq A $ for an $ H $-comodule algebra $ A $. This is achieved by constructing a …

Let $ Z $ be the center of a nonnoetherian dimer algebra $ A $ on a torus. We show that the
nilradical $\operatorname {nil} Z $ of $ Z $ is prime, may be nonzero, and consists precisely …

We explore the differential geometry of finite sets where the differential structure is given by
a quiver rather than as more usual by a graph. In the finite group case we show that the data …

To any trivalent plane graph embedded in the sphere Casals and Murphy associate a
differential graded algebra (dg-algebra), in which the underlying graded algebra is free …